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Improve Product Quality & Consistency while Meeting Compliance Requirements

Whether you need to comply with government regulations, meet customer specifications, or simply aim to exceed industry quality control standards, InfinityQS® solutions include built-in features to make your work easier.

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Process improvement methodologies like Six Sigma and Lean Manufacturing rely on solid data-collection plans and operational insight. InfinityQS gives you the ability to collect, aggregate, and analyze process and quality data to meet the demands of such programs.

Improve traceability and reduce recall risk
The ability to find any part or focus in on any process is a must for reliable traceability—and in turn, can help to prevent or reduce recalls. But how can you expect agile, flexible responses to data queries when half the work of gathering or locating data is still being done on clipboards and in spreadsheets? InfinityQS solves this problem with automated, responsive capabilities that simplify collecting, aggregating, and analyzing data, enabling you to find the information you need, easily and swiftly.

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InfinityQS quality and process optimization solutions provide automated, customizable, enterprise-wide quality- and process-data collection, analysis, and reporting so you can keep production moving and satisfy compliance and auditing demands. Keep throughput high and information at your fingertips.

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In today’s global market, you must juggle the details of multiple national and international regulations and compliance requirements. Meeting those expectations—and managing the reporting and downtime associated with audits and recalls—can drain time, energy, and resources. With InfinityQS, get automated notification when compliance checks are—or aren’t—performed and visibility into potential or actual failures.

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InfinityQS is ISO Certified 9001/2001, so you can have confidence in both quality and security controls.

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Electrical Devices

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Xbar and s (Xbar-s) Chart

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What are the Components of the Xbar-s Chart?

The Xbar chart (the upper chart in this figure) plots the average of individual values in a subgroup (i.e., the subgroup mean). The chart (the lower chart in the figure) plots the sample standard deviation of the individual values in the subgroup. This combined chart is sometimes referred to as Xbar-SD.

Xbar-s Charts for a Single Characteristic

A traditional Xbar-s chart is commonly used to monitor processes where the sampling strategy calls for large sample sizes, typically of 10 or more.

For example, this sample chart (taken from InfinityQS® ProFicient™ software) highlights subgroup 9 of 20 subgroups. You can see that the average of the subgroup’s plot points is 34.02 (top chart) and the standard deviation is 2.755 (lower chart).

Scroll down to learn how to use this chart.

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How to Use the Xbar-s Chart

Use the Xbar-s chart chart when your sample size is 10 or more (n≥10). This scenario is most common when a lot of data is available (or necessary) and the data acquisition cost is low.

For example, you might use this chart for data taken from Programmable Logic Controllers (PLCs) or other automated data-collection devices. Injection molding, multihead fill operations, and continuous high-speed production lines on which many measurements can be gathered quickly and affordably are all good environments for this type of chart.

Each of the special use case examples described on this page presume a large sample size (i.e., 10 or more).

Advantages and Disadvantages of Using the Xbar-s Chart

InfinityQS® software takes this chart technology to the next level by supporting multilevel Pareto charts—up to 10 levels deep.

Advantages

  • Very sensitive to small changes in the subgroup mean
  • Standard deviation is usually a more accurate indicator of process variation than is the range

Disadvantages

  • Requires gathering large amounts of data to calculate control limits

Decision Tree

Use the following decision tree to determine whether the Xbar-s chart is the best choice.
Scroll down to see special use examples.

Special Uses

Today, control charts are a key tool for quality control and figure prominently in Lean manufacturing and Six Sigma efforts.

Target Xbar-s Chart

Target Xbar-s charts can help you identify changes in the average and standard deviation of a characteristic. You can measure the characteristic across part numbers, but each part number must form a separate subgroup because target values change with the part number. Set the target values at the desired center, typically the center two-sided specifications.
  • Plot multiple parts or characteristics with similar variability on the same chart.
  • Assess statistical control for the process as well as for each of its parts or characteristics.
  • Detect very small process shifts.
  • Directly plot data from gauges that are zeroed out on target values (no data transformation or coding necessary).

Short Run Xbar-s Chart

Short run charts are used for short production runs. The short run Xbar-s chart can help you identify changes in the averages and standard deviation of multiple characteristics, even those with different nominals, units of measure, or standard deviations.

  • Summarize a great amount of data while still detecting small changes in process average.
  • Detect the difference between process- and product-specific variabilities.
  • Plot variations of multiple products, even those with differing standard deviations, nominals, or units of measure—all on one chart.

Group Xbar-s Chart

Group charts display several parameters, characteristics, or process streams on one chart. Group Xbar-s charts help you assess changes in averages and the standard deviation across measurement subgroups for a characteristic.

  • Compare the variations of a variety of products or characteristics.
  • See the difference between variations that are caused by changes in average and those caused by changes in the standard deviation.
  • Clearly detect characteristics that are priorities for attention.

Group Target Xbar-s Chart

The group target Xbar-s chart provides information about changes in process averages and the standard deviation across multiple measurement subgroups of similar characteristics that have a common process. Part numbers and engineering nominal values can differ across these characteristics.

  • Compare variations of multiple products or characteristics as well as similar characteristics with different averages.
  • See the difference between variations that are caused by changes in average and those caused by changes in the standard deviation.

Group Short Run Xbar-s Chart

The group short run Xbar-s chart enables you to spot changes in the process average and standard deviation across multiple characteristics in a short run environment.

  • Identify the difference between process- and product-specific variations.
  • Compare variations of multiple products or characteristics.
  • Analyze characteristics from a variety of parts, even those with different means, standard deviations, or units of measure.
  • See the difference between variations that are caused by changes in average and those caused by changes in the standard deviation.

Group Short Run Xbar-s Chart Example

Group Short Run Xbar-s Charts

Group short run Xbar-s charts enable you to spot changes in the process average and standard deviation across multiple characteristics in a limited production run. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group short run Xbar-chart works.

Group Short Run Xbar s Control Chart Example

Figure 1. Mechanical pencil with three key characteristics.

Case Description

A company manufactures mechanical pencil lead. There are three key characteristics (see Table 30.5).

  1. Break force—The amount of pressure it takes to break the lead (extended 1.5 mm) at a 38° angle with the force applied 3 cm from the lead rip
  2. Drag—A proprietary measure of how smoothly the lead releases onto a given paper
  3. Diameter—The diameter of the lead

Table 1. Upper and lower specification limits for three mechanical pencil lead key characteristics.

Control Chart Case Description

The manager wishes to monitor the stability of all three key characteristics on the same chart.

Sampling Strategy

Because production volume is very high and three different characteristics are to be monitored, a group short run Xbar-chart is selected. Ten leads are tested every 30 minutes.

Target Values

Preliminary tests on all three key characteristics were conducted. The purpose of the tests was to establish target values for the group short run charts to be used. The target values are found in Table 2.

Table 2. Target X and target s values for the three mechanical pencil lead key characteristics.

Control Chart Target Values

Data Collection Sheet

Table 3. Data collection sheet for the group short run Xbar-s chart pencil lead example. MAX and MIN plot points are shown in bold.

Xbar s Control Chart Data Collection Sheet 2
Xbar s Control Chart Data Collection Sheet 3
Xbar s Control Chart Data Collection Sheet 3

Group Short Run Xbar-s Chart

Group Short Run Xbar s Chart

Figure 2. Group short run Xbar-chart for the pencil lead example. Three key characteristics are being monitored on the same chart.

 

Chart Interpretation

Group short run s chart: All three characteristics—break force (A), drag (B), and lead diameter (C)—appear to randomly fluctuate in the MAX and MIN positions. This indicates that the initial target values were good estimators for all of the characteristics.

Group short run Xbar chart: It appears that all three key characteristics are randomly fluctuating in the MAX and MIN positions. This means that the initial target values were good estimators of the actual means for each of the three characteristics.

Recommendations

Group short run s chart: Continue using the initial target s values for all three characteristics. The charts may look good, but only the capability studies will determine if the characteristics are meeting engineering requirements.

Group short run Xbar chart: Continue using the initial target X values. No recalculation is necessary. The process averages appear stable and predictable. Continue to collect data. If the process remains stable, reduce sampling frequency.

Estimating the Process Average

Estimates of the process average should be calculated separately for each characteristic on each part on the group short run charts. The estimate of the process average for break force can be found in Calculation 1.

process average for characteristic A
Calculation 1. Estimate of the process average for characteristic A, break force.

Estimating Sigma

Estimates of sigma are also calculated separately for each characteristic on each part on the group short run charts. Continuing with characteristic A, see Calculations 2 and 3.

S calculation
Calculation 2s calculation for characteristic A, break force.

process standard deviation
Calculation 3. Estimate of the process standard deviation for characteristic A, break force.

Note: To ensure reliable estimates of both the process average and process standard deviation, k needs to be at least 20. In this example, k is only nine. Therefore, the estimates here and in Table 4 are shown only for illustration purposes.

 

Calculating Process Capability and Performance Ratios

Calculations 4, 5, and 6 show the capability calculations for break force, characteristic A.

Cp formula for percent solids
Calculation 4. Cp calculation for characteristic A, break force.

Cpk upper formula six sigma
Calculation 5. Cpk upper for characteristic A, break force.

Cpk lower formula six sigma
Calculation 6. Cpk lower calculation for characteristic A, break force.

Group Short Run Xbar-s Chart Advantages

  • Graphically illustrates the variation of multiple product or process characteristics relative to each other.
  • Characteristics from different parts with different means, different standard deviations, and different units of measure can all be analyzed on the same chart.
  • Separates variation due to changes in the average from variation due to changes in the standard deviation.
  • Separates variation due to the process from variation that is product specific.

 

Group Short Run Xbar-s Chart Disadvantages

  • No visibility of characteristics that fall between the MAX and MIN plot points
  • Cannot detect certain nonrandom conditions because the group charts described here have no control limits
  • Lots of calculations

 

An Additional Comment About the Case

Additional statistics and process capability and performance calculations for key characteristics B and C are shown in Table 4.

Table 4. Additional statistics and process capability and performance calculations for the drag and diameter key characteristics.

process capability calculations

When you use SPC software from InfinityQS, consuming the information provided by group short run Xbar-charts becomes faster and easier than ever. See how this type of analysis is surfaced in InfinityQS solutions.

FOOTNOTE:
1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

Group Target Xbar-s Chart Example

Group Target Xbar-s Charts

Group target Xbar-s charts provide information about changes in process averages and the standard deviation across multiple measurement subgroups of similar characteristics that have a common process. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group target Xbar-chart works.

Chart Example group target Xbar s

Figure 1. Three hole-location measurements from a rocker.

Case Description

The rocker shown in Figure 1 is machined from an iron casting. There have been complaints from field mechanics that the rockers are not interchangeable and that the holes do not always line up with mating parts. To monitor the uniformity of the hole locations, the operators would like to use a chart at the milling machine to track the variability of the three hole locations.

Sampling Strategy

Because production volume is very high and all the measurements represent hole locations of different distances created on the same machine, a group target Xbar-chart is selected. Ten rockers are measured every hour.

Data Collection Sheet

Table 1. Group target Xbar-s chart data collection sheet for three hole locations on a rocker. MAX and MIN plot points are shown in bold.

group target Xbar s Control Chart Data Collection Sheet 2
group target Xbar s Control Chart Data Collection Sheet 3
group target Xbar s Control Chart Data Collection Sheet 4

Group Target Xbar-s Chart

Group Target Xbar s Control Char

Figure 2. Group target Xbar-chart representing three different hole locations on the same part.

 

Chart Interpretation

Group s chart: Location a appears in the MAX position in every group. This indicates that location a has the largest standard deviation. Locations b and c appear randomly in the MIN position, meaning that location b and c’s standard deviation values are both similar to one another and smaller than location a’s.

Note: The centerline on the group s chart is the average of all the sample standard deviation values on the data collection sheet.

Group target Xbar chart: The coded Xbar for location a appears in the MAX. position in every group and its value is always positive. This indicates that the average hole location at location a is consistently higher than the engineering nominal (target) value.

Location appears in the MIN position in all nine groups and its value is always negative. This means that the average hole location distance at location c is consistently lower than its engineering nominal (target) value.

Note: The centerline on the group target Xbar chart is the average of all the coded Xbar plot points in the data collection sheet.

 

Recommendations

  • The group target Xbar chart reveals two consistent problems: Location a is always wider than target, and location c is always closer. This type of problem is fixed by changing the location of one or more holes during the job setup. The chart itself does not indicate which hole to relocate. A logical place to begin investigation is with hole 1 because its location affects both key locations a and c.
  • Looking at the group s chart, the distance between holes 1 and 3 (hole location a) varies more than the other hole relationships. This also means there is excess variation in the horizontal axis. Operators should verify this assumption with process engineers and remedy the problem..

 

Estimating the Process Average

If all of the locations on the group target Xbar chart were behaving randomly, a single estimate of the process average could be used to estimate the process average for all locations. However in this case, the group target Xbar chart does not exhibit random behavior.

Given nonrandom patterns on a group target Xbar chart, estimates of the process average should be calculated separately for each characteristic or location. This is illustrated in Calculation 1 using data from hole location a.

group target Xbar s process average estimate

Calculation 1. Estimate of the process average for hole location a.

Estimating Sigma

Estimates of sigma are also calculated separately for each characteristic or location on the group target chart. Continuing with hole location a, see Calculations 2 and 3.

group target Xbar s formula standard deviation

Calculation 2. Calculation of for use in estimating the process standard deviation for hole location a.

group target Xbar s process standard deviation

Calculation 3. Estimate of the process standard deviation for hole location a.

Note: To ensure reliable estimates, the number of groups should be at least 20. In this example, the number of groups is only nine. Therefore, the estimates here and in Table 2 are for illustration purposes only.

 

Calculating Process Capability and Performance Ratios

The Cp and Cpk calculations for hole location a are shown in Calculations 4, 5, and 6.

group target Xbar s calculating Process Capability Performance
Calculation 4. Cp calculation for hole location a.

group target Xbar s Cpk Formula Upper Calculation
Calculation 5. Cpk upper calculation for hole location a.

group target Xbar s Cpk Formula Lower Calculation
Calculation 6. Cpk lower calculation for hole location a.

Group Target Xbar-s Chart Advantages

  • Simultaneously illustrates the variation of multiple product or process characteristics.
  • Similar characteristics with different averages can be analyzed on the same chart.
  • Separates variation due to changes in the average from variation due to changes in the standard deviation.
  • Multiple characteristics can be tracked on one chart.

 

Group Target Xbar-s Chart Disadvantages

  • No visibility of the characteristics that fall between the MAX and MIN plot points.
  • The use of negative numbers can be confusing.
  • Cannot detect certain nonrandom conditions because the group target charts described here have no control limits.

 

An Additional Comment About the Case

The process capability and performance values for hole locations b and c are shown in Table 2.

Table 2. Summary statistics and process capability and performance ratios for hole locations and c.

process capability performance ratio

When you use SPC software from InfinityQS, consuming the information provided by group target Xbar-charts becomes faster and easier than ever. See how this type of analysis is surfaced in InfinityQS solutions.

FOOTNOTE:
1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

Group Xbar-s Chart Example

Group Xbar-s Charts

Group Xbar-s charts help you assess changes in averages and the standard deviation across measurement subgroups for a characteristic. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group Xbar-chart works.

Group Xbar s Chart Example
Figure 1. Three width measurements from a yoke.

Case Description

This yoke is machined from an aluminum casting. There have been complaints from the assembly department that some of the yokes have a taper on the inside width. To monitor the uniformity of the inside widths, a group chart is set up at the milling machine to track the width at locations a, b, and c.

Sampling Strategy

Because the production volume is very high, and the same characteristic is being measured at three different locations on the part, a group Xbar-s chart is selected. Ten yokes are measured every hour.

Data Collection Sheet

Table 1. Data collection sheet for the group Xbar-s chart. MAX and MIN plot points are shown in bold.

Group Xbar s Chart Data Collection Sheet 1
Group Xbar s Chart Data Collection Sheet 2
Group Xbar s Chart Data Collection Sheet 3

Group Xbar-s Chart

Chart Example group Xbar s

Figure 2. Group Xbar-s chart representing three different yoke width locations.

 

Chart Interpretation

Group s chart: Location a appears in the MAX position for all groups. This suggests that location a has the largest standard deviation. Locations b and c appear randomly in the MIN position. This indicates that locations b and c have similar standard deviations and they are less than location a’s.

Note: The centerline on the group s chart is the average of all the 5 values on the data collection sheet.

Group Xbar chart: The difference between the MAX and MIN for each group represents taper within the yokes. Locations a, b, and c appear randomly in the MAX position. However, location a appears five out of nine times in the MIN position. This might indicate that location a has a smaller diameter than either of the two other locations. However, this supposition is not as strong as it would be if location a represented the MIN position for all groups.

Note: The centerline on the group Xbar chart is the average of all the Xbar plot points found on the data collection sheet.

 

Recommendation

The repeated presence of location a in the MAX position in the group s chart may be the result of the inability of tooling to hold the work piece consistently during the manufacturing of the yokes. Notice that location a is found at the end of the yoke. This may signify the need for tooling changes that will hold the outer ends more rigidly during manufacturing.

 

Estimating the Process Average

Process average estimates should be performed separately for each characteristic or location on the group chart (see Calculation 1).

Group Xbar and s chart process average

Calculation 1. Estimate of the process average for yoke width at location a.

Estimating Sigma

Estimates of sigma are also calculated separately for each characteristic or location on the group chart. Continuing with yoke width location a, see Calculations 2 and 3.

average sample standard deviation

Calculation 2. Calculation of the average sample standard deviation for yoke width location a.

Estimated standard deviation

Calculation 3. Estimated standard deviation for yoke width location a.

Note: To ensure reliable estimates, the number of groups should be at least 20. In this example, the number of groups is only nine. Therefore, these estimates and those found in Table 2 are only for illustration purposes.

 

Calculating Process Capability and Performance Ratios

Calculations 4, 5, and 6 show the process capability and performance calculations for yoke width location a.

Cp calculation width
Calculation 4. Cp calculation for width location a.

Cpk upper calculation
Calculation 5. Cpk upper calculation for width location a.

Cpk lower calculation
Calculation 6. Cpk lower calculation for width location a.

Group Xbar-s Chart Advantages

  • Graphically illustrates the variation of multiple product or process characteristics simultaneously and relative to each other.
  • Pinpoints the characteristics that are in need of the most attention.
  • Separates variation due to changes in the average from variation due to changes in the standard deviation.
  • Multiple measurement locations can be tracked on one chart.

 

Group Xbar-s Chart Disadvantages

  • No visibility of the characteristics that fall between the MAX and MIN plot points.
  • Cannot detect certain out-of-control conditions because the group charts described here have no control limits.
  • Given the large amounts of data used in charts, efficient analysis typically requires software.

 

An Additional Comment About the Case

The process capability and performance ratio calculations for yoke widths at locations b and are shown in Table 2.

Table 2. Summary statistics and process capability and performance ratios for yoke widths at locations b and c.

Group Xbar and s chart

When you use SPC software from InfinityQS, consuming the information provided by group Xbar-charts becomes faster and easier than ever. See how this type of analysis is surfaced in InfinityQS solutions.

FOOTNOTE:
1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

Short Run Xbar-s Chart Example

Short Run Xbar-s Charts

Short run Xbar and s (Xbar-s) charts can help you identify changes in the averages and standard deviation of multiple characteristics in a limited production run. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a short run Xbar-chart works.

Short Run Xbar s Chart Example

Figure 1. Delta torque is a performance key characteristic on self-locking fastener systems.

Case Description

Torque is tested on self-locking nuts using precision stud standards and production nuts. During production, the nuts are slightly deformed so that the threads create an interference or locking fit with the stud. The run-on torque is the average prevailing torque while turning the nut on the stud seven clockwise revolutions. The runoff torque is the maximum force it takes to turn the nut back off the stud one counterclockwise revolution. The delta torque is the run-on torque minus the run-off torque. Each fastening system has its own minimum delta torque requirements and the standard deviations are expected to vary from system to system.

Sampling Strategy

Torque tests are performed for each batch of locking nuts. Ten samples are tested from each batch. To monitor the delta torque consistency, regardless of the nut/bolt locking system, a short run Xbar-chart is selected. This is the appropriate chart because the subgroup sizes are large and the standard deviations are different from system to system.

Target Values

Before a short run chart can be used, target values must first be defined.

Locking System A

System A has previously been maintained using traditional Xbar-charts. On the most recent set of in-control charts, the centerline on the Xbar chart was 2.920. The centerline on the chart was 0.089. Therefore, these centerlines are used as target values for system A.

Target values for locking system A
Figure 2. Target values for locking system A.

Locking System B

The consistency of locking system B has never been evaluated with a control chart. However, quality assurance personnel have taken 28 delta torque measurements at some time in the past. Equation 15.14 was used to convert the sample standard deviation from those 28 measurements into the targets found in Figure 3.

Target values for locking system b
Figure 3. Target values for locking system B.

Locking System C

Like system A, Rocking system C has previously been evaluated using traditional Xbar-charts. On the most recent set of in-control charts, the centerline on the Xbar chart was 5.125. The centerline on the s chart was 0.337. Therefore, these centerlines are used as target values for system C (see Figure 4).

Target values for locking system b
Figure 4. Target values for locking system C.

Data Collection Sheet

Table 1. Delta torque data sheet and plot point calculations.
Short Run Xbar s Chart Data Collection Sheet 1
Short Run Xbar s Chart Data Collection Sheet 2
Short Run Xbar s Chart Data Collection Sheet 3

Short Run Xbar-s Chart

Chart Example short run Xbar s

Figure 5. Delta torque short run Xbar and s control charts for locking systems A, B, and C.

 

Chart Interpretation

Short run chart: If evaluating product-specific variation, locking system A’s delta torque seems to be behaving randomly. All eight of system B’s plot points fall above the centerline with one of them falling above the UCL. System C’s delta torque favors the high side with one plot point beyond the UCL. Overall, the process reveals a run of 9 plot points above the centerline that occur across three product lines (subgroups 13 through 20).

Short run Xbar chart: All seven of system A’s plot points fall below the centerline with three of them falling below the LCL. Seven of system B’s eight plot points are situated above the centerline with three above the UCL. System C appears to be behaving randomly. Looking at patterns across locking systems, there is a gradual decrease in the average from plot point 6 through 12. Also, it looks as though the average has shifted higher between plot points 13 and 20.

Recommendations

Note: Plot point patterns above and below the centerlines and beyond the control limits are present, but the action to take depends entirely on how the target values were estimated.

 

Locking System A

Short run s chart: The target came from past control charts, therefore, the fact that the plot points are behaving randomly indicates that the standard deviation has not changed since data were last recorded.

Short run Xbar chart: The target X came from past charts, therefore, the run below the centerline indicates the delta torque has decreased since data were last recorded. This is an assignable cause and should be investigated. If the shift is found to be desirable, deliberate, and permanent, the target X should be recalculated based on system A’s current overall average. If the shift is found to be an unwanted condition, do not recalculate target X. Instead, eliminate the cause of the downward shift.

Locking System B

Short run chart: The target s came from past quality assurance records. The run above the centerline, therefore, indicates that the standard deviation has significantly increased since data were last recorded. This may be an assignable cause and should be investigated. If the shift is found to be an unwanted condition, do not recalculate target s. Instead, eliminate the cause of the increased variability.

Short run Xbar chart: The target came from quality assurance records, therefore, the run above the centerline indicates the delta torque has increased since data were last recorded. This may be an assignable cause and should be investigated. If this significant increase in delta torque is desirable, then the target X should be recalculated based on system B’s current overall average. If the shift is unwanted, do not recalculate target X. Instead, eliminate the assignable cause for the increase in the delta torque average.

Locking System C

Short run s chart: Because the target s was based on the centerline from an older, in-control s chart, the run above the centerline indicates that the process standard deviation has increased significantly since the last time the system C product was manufactured. This should be treated as an assignable cause because the target is based upon actual data. If the increase in standard deviation for system C is expected to be a permanent change, then the target should be recalculated based on the current overall average standard deviation (see Calculation 1). Otherwise, if the assignable cause is to be removed to reduce the current amount of variation, the old target should be saved to represent the current expected level of variability.

Locking System C

Calculation 1. Recalculating locking system C’s target s based on current data from control chart. This is done only if the change in variability is expected to be a permanent one.

Short run Xbar chart: The target has been obtained from a recent in-control chart, and the plot points are behaving randomly. This indicates that the initial target X was a good estimator of the actual delta torque. There is no need to recalculate system C’s target X.

Estimating the Process Average

Estimates of the process average should be calculated separately for each characteristic or part on short run Xbar-s charts. In this case, estimates of the process average should be calculated separately for each different locking system. Calculation 2 shows the calculation for the estimate of the overall average of locking system B.

estimating process average

Calculation 2. Estimate of the process average for locking system B.

Estimating Sigma

Estimates of sigma are also calculated separately for each characteristic or location represented on short run Xbar-s charts. In this case, estimates of the process standard deviation should be calculated for each different locking system. Estimates of the process standard deviation for locking system B are found in Calculation 3.

Sigma

Calculation 3. Calculation of for locking system B based on current data from the short run s control chart.

calculating process standard deviation
Calculation 4. Calculation of the estimate of the process standard deviation for locking system B.

Note: To ensure reliable estimates, k needs to be at least 20. In this example, k is only 8. Therefore, the estimates here and in Table 2 are used for illustration purposes only.

 

Calculating Process Capability and Performance Ratios

The Cpk lower calculation for locking system B is shown in Calculation 5. Because there is only a minimum specification, no Cp or Cpk upper value is calculated for locking system B.

Cpk calculation formula
Calculation 5. Cpk lower calculation for fastener system B delta torque.

Short Run Xbar-s Chart Advantages

  • Graphically illustrates the variation of multiple products with different nominals, different standard deviations, and even different units of measure all on the same chart.
  • Separates sources of process variability from sources of product variability.
  • Due to the large sample sizes, the short run Xbar chart is sensitive to small changes in the process average.
  • Summaries large amounts of data.

 

Short Run Xbar-s Chart Disadvantages

  • Requires software to effectively handle large amounts of data.
  • The use of negative numbers and unitless ratios may be confusing at first.
  • X, s, and process standard deviation estimates must be calculated separately for each characteristic represented on the chart.

 

Additional Comments About the Case

  • The process capability and performance ratio calculations for locking systems A and C are found in Table 2.
  • Summary statistics and Cpk lower values for systems A and C are based on the actual data from the data collection sheet (Table 1). In addition, no Cp or Cpk upper values are found in Table 2 because the locking systems all have one-sided specifications.

Table 2. Additional summary statistics and process performance ratios for locking systems A and C.

process performance

When you use SPC software from InfinityQS, consuming the information provided by short run Xbar-charts becomes faster and easier than ever. See how this type of analysis is surfaced in InfinityQS solutions.

FOOTNOTE:
1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

Using the Target Xbar-s Chart: Example

See how the target Xbar-chart enables plant-floor personnel to maintain tight tolerances on high-volume production lines.

How Do You Use Target Xbar-s Charts?

Target Xbar and s (Xbar-s) charts can help you identify changes in the average and standard deviation of a characteristic. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a target Xbar-chart works.

xbar and s control chart example

Figure 1. Rivet head height is a key characteristic. The measurement is taken with the aid of a gauge block.

Case Description

Rivet head height is a key characteristic. The height is measured off a gauge block. If the height is too low, the installed rivet will recede below the surface. If it is too high, it will protrude. Either case requires rework and is unacceptable. Three different types of rivets are manufactured, each with different target head heights and tolerances. In this example, the target Xbar-s chart allows operators to maintain extremely tight tolerances for a high-volume, high-speed production process.

Bring SPC Charts Up to Speed

This example provides a deep dive into the manual calculations behind the target Xbar-s chart. InfinityQS® solutions—ProFicient™ and Enact®—automate chart creation and help you optimize processes faster.

LEARN MORE ABOUT MODERN SPC SOLUTIONS

Table 1. Target head heights and specifications.

target xbar and s chart example

Sampling Strategy

Several rivet types are to be plotted on the same chart, but because only one characteristic, head height, is to be controlled, use of a target chart would be appropriate. The production volume is extremely high (thousands per hour), the data collection is quick, and the analysis is being done with the assistance of computer software. For all these reasons, a target Xbar-s chart is selected.

To determine how often measurements should be taken, a header mechanic is surveyed. It is revealed that adjustments to the equipment affecting head height are made about every hour. To capture the effects of these adjustments, samples of 10 are taken every 10 minutes.

Data Collection Sheet

Table 2. Data collection sheet for three different rivet head heights.

target xbar and s charts example 1

target xbar and s charts example 2

target xbar and s charts example 3

Target Xbar-s Chart

control chart constants

Figure 2. Head height target Xbar-s control chart.

Control Limit Calculations

xbar and s control charts

Calculation 1. Calculations for target Xbar chart.

xbar and s control chart

Calculation 2. Calculations for s chart.

Chart Interpretation

s chart: The chart is in control. This shows that the sample standard deviations of head heights for all three rivet types are similar.

Target Xbar chart: This chart is also in control. There are no indications of assignable causes. This means that the difference between the average head heights of all three rivet types and their respective targets is about the same.

Recommendations

  • Based on the target Xbar chart, the process is running very close to target regardless of rivet type. This is a situation where the process should not be adjusted.
  • Even though the standard deviations are similar for all three rivet types, one will still need to calculate separate Cp and Cpk ratios. This is necessary because the engineering tolerances are different for each rivet type.

 

Estimating the Process Average

Because the target Xbar chart is in control, the process average for all rivet types can be estimated using the coded X.

target xbar and s chart
Calculation 3. Estimate for the coded overall process average rivet head height (to be used in Cpk calculations for all three rivet types).

Estimating Sigma

Because the s chart is in control, the process standard deviation can be estimated for all three rivet types using the formula found in Calculation 4.

xbar and s
Calculation 4. Estimating sigma using s.

Calculating Process Capability and Performance Ratios

These ratios are calculated using coded data. The coded nominal for the head height characteristic is zero. Therefore, for rivet A, the coded USL is +10 and the coded LSL is –10. Following are calculations for the rivet A head height.

xbar and s target
Calculation 5. Cp calculation for rivet A head height.

xbar and s chart calculation
Calculation 6. Cpk upper calculation for rivet A head height.

xbar and s charts
Calculation 7. Cpk lower calculation for rivet A head height.

Target Xbar-s Chart Advantages

  • Multiple parts or characteristics can be plotted on the same chart (provided they all exhibit similar variability).
  • Data from gauges that are zeroed out on their target values can be plotted directly on the target Xbar without data coding or data transformation.
  • Statistical control can be assessed for both the process and each unique part and/or characteristic being made in the process.
  • Due to the large subgroup size, the Xbar chart is very sensitive to small process shifts.

 

Target Xbar-s Chart Disadvantages

  • Requires software to efficiently handle the large amounts of data.
  • The use of coded negative numbers can sometimes be confusing.
  • When interpreting the target Xbar chart, both the zero line and the coded X must be taken into account. This accounts for some added complexity when interpreting the chart.

 

Additional Comments About the Case

  • Process capability and performance calculations for the B and C rivets are shown in Table 3.
  • Because the target Xbar-s chart proved to be in control, the only values that change when calculating the capability ratios are the specification limits. The coded X and sigma values used to calculate Cp and Cpk ratios are the same for all three rivet types.

Table 3. Cp and Cpk calculations for B and C rivets.

xbar and s chart example

FOOTNOTE:
1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

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What to Expect

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Quality Team

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Extend and Empower Your Quality Team

In modern manufacturing organizations, quality professionals seek to tightly manage every step in every process to ensure consistent quality—a task that becomes more challenging as production lines cross staff, processes, and plants.

Using statistical process control (SPC) for quality improvement can alleviate some of the complexity. SPC brings a systematic approach to data collection and analyses, no matter where they occur. Quality team leaders set the expectations for data collection (i.e., what, when, and how), and establish acceptable deviations. Unfortunately, traditional quality control in manufacturing ends there. The value of that data is often limited to a single use, verification of compliance, or an adjustment justification.

A central data repository extends the benefits of SPC by making the quality data you collect accessible throughout the organization, whether that’s on the plant floor or in the executive board room. With a single repository for quality data, commonly “siloed” information comes together to create a singular, company-wide picture of quality.

Making quality data consistent, accessible, and actionable empowers every team member to put quality first.

Usable, accessible quality data empowers everyone, from the plant floor to the executive board room, to be part of the quality team.
QualityDashboard_Thumb

Get Everyone on the Quality Team

Standardization and centralization of data establishes a common language—and expectation—surrounding quality that cascades throughout the organization. When every team member is using the same playbook, some of the complexity dissipates. In its place, manufacturing organizations can introduce ways to improve quality and productivity.

Quality-focused teams can realize greater benefits from their statistical process control efforts.

Eliminate error-prone processes

Manual data collection can lead to “garbage in, garbage out,” wasting the time and resources it takes to collect and analyze the data. Handwritten data can be difficult to interpret, and paper reports can become lost or damaged. If data is missing or indecipherable during an audit, the results can be costly.

InfinityQS solutions enable semi-automated and automated data collection, as well as automated alerts and notifications, to ensure checks are completed and data is accurate. And centralizing your data in a single repository helps you build a clear picture of quality across the organization.

Empower real-time decision-making

Siloed data leads to slower decision-making. In contrast, InfinityQS quality improvement solutions make it easy for you to access data in real time—by production line, plant, or region—at the same pace you need to make quality decisions. Operations managers and quality team members know the moment an issue arises so they can take steps to preserve quality or avoid costly missteps.

Plan more efficiently

With a centralized data repository, empowered users can create and pull reports when they need them, without waiting for IT to merge data from multiple systems or manage a massive export. With accurate and complete data, you can easily plot a continuous improvement journey.

Identify high-impact quality improvements

With accessible, data-backed insights, quality teams can find the most influential quality initiatives to undertake as a company—by region, product, or plant. InfinityQS solutions help you spot transformative opportunities that might otherwise be buried in spreadsheets or stuck in an operational silo. And purpose-built analytical tools help you determine which initiatives will deliver the biggest and fastest ROI.

Save valuable time and money

Quality control in manufacturing is intended to save time and money—not drain resources or become just one more cost center. Quality management software solutions from InfinityQS help your whole quality team increase profits by improving some of the costliest manufacturing metrics like scrap and rework, unplanned downtime, overtime, defect costs, and warranty claims.

Empowered Quality Teams Improve Manufacturing Quality

Ready to empower every team member to put quality first? Take a peek at the features, analytics, dashboards, and reports in InfinityQS software to see how you can improve quality using data you already have.

Improve-Manufacturing-Quality

Connect Your Teams, Improve Your Quality

Putting actionable information into the hands of every empowered team member—from operators to quality professionals to executive leaders—prevents quality disruptions and moves the organization toward quality manufacturing best practices. Working together, you can achieve stronger quality outcomes that transform the entire enterprise, such as:

  • Optimized production
  • Cost, defect, and recall reduction
  • Reduced risk and downtime
  • Improved product compliance and lower audit costs
  • Better yields at the process, plant, regional, and enterprise levels

InfinityQS quality improvement solutions bring data and people together throughout the manufacturing process. The result is greater efficiency, better product consistency, and overall higher manufacturing quality.

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What to Expect

  • Free 20-minute call with a product expert
  • Explore which solutions best suit your needs
  • No-pressure conversation
  • Get a live, personalized demo

Quality Metrics

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Manufacturing Excellence Starts with the Data You Already Have

Modern manufacturers have two choices: to simply meet quality and regulatory standards or to pursue manufacturing excellence and reset the bar. Which do you choose?

The insight you need to break through quality barriers and transform your manufacturing organization is within reach. It’s in your quality metrics.  

The metrics you measure are more than just report cards and to-do lists. They can help you adapt, thrive, and thrill customers with reliably high quality. The challenge is being able to see into that vast amount of data to determine which quality initiatives should rise to the top.

The key is to standardize and centralize your quality data in a single repository. Once performance data from different quality systems are unified, they can be turned into manufacturing intelligence.

Stop solving problems and start pursuing excellence. Use quality metrics to launch a perpetual cycle of continuous improvement.

QualityMetrics_Dashboard

Get the Total Quality Picture

What would happen if you only read 2% of your emails? You’d miss a lot.

That’s exactly what many manufacturing organizations are doing with their collected data; they dig deep into exception data and ignore the majority of their quality metrics. By doing so, they miss opportunities to make substantive, system-wide improvements.

InfinityQS quality improvement software aggregates a variety of quality metrics—and yes, this includes in-spec data, so it’s easy to compare performance across lines, parts, plants, and other key factors. Whether data are collected manually or through automation, they all flow into one place. Then the data are standardized so access to the information and analysis becomes easy, and you can see the “big picture” of quality across the organization.

Statistical process control (SPC)-driven dashboards and control charts bring quality priorities into focus. With access to this clarified data in real time, your busy executives can identify opportunities for huge improvements in quality, customer satisfaction, and profitability.

QualityMetrics_DataGrading

Better Decisions Lead to Better Quality

InfinityQS solutions help leaders model process capability so they can evaluate the impacts of quality improvement initiatives—and prioritize those that will have the most value.

Data stream grading, for example, enables executives to visually expose and isolate those areas of potential improvements. All streams of data are given a score based on actual performance versus expected performance, giving leaders a clear picture of what’s working, where they need to deploy Six Sigma support, and what they stand to gain.

Simple color-coded matrices show leaders where to capture “quick wins” and which processes will deliver transformational improvement.

With detailed metrics at their fingertips, executives gain visibility across the entire enterprise. Quality excellence that’s achieved in one plant or line can be replicated across the organization to maximize the impact and multiply return on investment (ROI). Even with limited resources, quality manufacturing leaders can turn data into intelligence and better-informed decisions.

Which Quality Metrics Matter Most?

All of your quality metrics matter—not just the defects or “lessons learned.” InfinityQS quality improvement solutions collect and combine all of your quality data into a single system so you can compare and improve performance across the enterprise. See what’s happening in your organization in real time and over time.

QualityMetrics_Executives

See What’s Ahead to Stay Ahead

InfinityQS helps manufacturers prevent quality issues rather than simply respond to them. Built to support quality manufacturing with real-time SPC, InfinityQS software gives leaders the information they need to predict quality outcomes, when and where they need it.

Dashboards transform key quality data into digestible summaries, so quality leaders can take proactive steps to reduce risk, increase efficiency, improve profitability, and produce top-quality products.

In modern manufacturing, it’s not enough to know what happened yesterday. To achieve quality excellence, you need to know what’s happening right now, what will happen if you take action, and where to begin.

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  • Explore which solutions best suit your needs
  • No-pressure conversation
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Quality in Real Time

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Close the Gap between Insight and Action

Statistical process control (SPC) standardizes the processes that manufacturers use to collect and analyze quality data. Using SPC, manufacturers become better at predicting outcomes and improving their quality manufacturing processes.

When teams are working to improve quality in real time, they reduce the lag between data collection and proactive corrective actions.

InfinityQS solutions enable real-time data to flow seamlessly into existing workflows right “out of the box.” Once quality data are entered, they are saved to the unified data repository, building a comprehensive view of quality that can be dissected and analyzed across any number of factors, from product code to production line or geographic site.

The information is accessible and actionable too. Using easy-to-read dashboards and alerts, empowered team members can see where they need to focus their attention—right now—to protect quality and eliminate waste.

Time is money. InfinityQS solutions ensure that critical quality data is collected, analyzed, and put to use immediately.

Enable teams to take action and improve quality in real time.

QualityinRealTime_Alert

Spot Quality Issues Before They Become Problems

To protect your company’s reputation and earning potential, you need to predict and prevent quality issues before they become full-scale problems. Once products fail in the field, are recalled, or generate customer complaints, recovery can be difficult (and costly) for manufacturers.

InfinityQS quality improvement solutions create a centralized and standardized place for your quality manufacturing data to reside. Real-time data collection, dashboard-level reporting, and automated alerts empower quality teams to act on the data in real time to head off quality problems.

Intervening early saves manufacturers from costly rework, scrap, waste, and upset customers. InfinityQS software gives operators, quality teams, and executives the information they need to control quality and maintain continuous improvement.

When Do You Need Quality Data?

To maintain top quality manufacturing, operators and quality teams need data in real time. InfinityQS enables data collection, analysis, and reporting in real time so you can take steps to consistently protect quality. Right now.

QualityRealTime_Line

Advantages of Quality in Real Time

The ability to monitor and analyze real-time data from anywhere can save manufacturers millions of dollars. With real-time data, manufacturers can reduce waste and scrap, prevent defects and recalls, and empower operators to protect quality.

On the Plant Floor: Reduce Waste, Prevent Defects, and Empower Operators

Machines or processes that are producing out-of-spec products or parts can waste time and materials, and even lead to product recalls. InfinityQS quality improvement solutions help manufacturers identify issues and pinpoint problem areas in real time and along the entire manufacturing process—not just during final testing.

InfinityQS helps manufacturers continually measure and improve their operations by:

  • ensuring quality checks are completed consistently and accurately
  • catching issues and non-conforming products as early as possible
  • automatically alerting operators when a process, machine, or product falls out of spec
  • drilling down into issues and trends so variations can be resolved faster

InfinityQS solutions enable users to monitor and respond to real-time quality data from any location, any time. Your data are stored in a centralized repository and standardized to accommodate detailed investigations into defect codes, shifts, customer codes, employees, lot numbers, or parts.

InfinityQS solutions give operators, engineers, and plant managers the tools and insight they need to identify, prioritize, and drive quality improvement.

QualityRealTime_Computer

Across the Enterprise: Turn Information into Strategy

At the corporate level, one person may oversee several products, plants, or regions. A unified data repository that’s updated and accessible in real time helps off-site managers stay tightly connected to daily operations—even at remote facilities.

When quality leaders have accurate and timely information at their fingertips, manufacturing organizations gain the following benefits:

  • Speed—Quality leaders can pull information, track trends, and respond to audits in a fraction of the time required with manual or siloed data management solutions.
  • Powerful analytic capabilities—Leaders can compare products, shifts, processes, and sites in a single chart or dashboard without performing exports or complex calculations.
  • Strategic insight—With the ability to analyze historical and aggregated data, quality managers can develop best practices and uncover new approaches to achieve quality that provides a competitive advantage.
  • Confidence—Managers can verify, in real time, that quality manufacturing processes are being followed precisely across lines, shifts, and sites.

A Food and Beverage Manufacturer Cut $2.2M in Waste with On Demand SPC Software

A leading North American consumer packaged Food and Beverage company needed to decrease plant-to-plant manufacturing variations and reduce waste. The company leveraged InfinityQS SPC-driven and cloud-based quality management software to pool real-time manufacturing data from six sites and a corporate lab into a single, secure data repository.

With immediate access to real-time performance data, the quality assurance team was able to quickly find and respond to fluctuations in data. See what they uncovered—and how it changed the business.

Read the case study

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What to Expect

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Quality Dashboards

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Put Your Quality Data to Work

Quality dashboards make quality data quick to access and easy to understand. Manufacturers collect enormous amounts of information throughout the manufacturing process to measure and protect the quality of their products. But “measuring what matters” only benefits quality when the information is accessible to decision-makers.

Quality improvement dashboards provide high-level summaries of important metrics without forcing users to dig for details. And dashboards can be tailored to suit the demands of different roles. For example, plant floor operators can focus on a quality alert or metrics for a specific line. Meanwhile, corporate users might investigate historical or enterprise-wide data to uncover new opportunities to improve company profits.

Once built, dashboards and data collections can change how people work in a quality manufacturing environment. Everyone can see how the organization is performing and how their actions affect quality. Armed with actionable information, staff can work more effectively and efficiently toward quality outcomes.

Quality dashboards change the way people work by making it easy for them to quickly find information and take action.
QualityDashboards_Line

 

Use Quality Dashboards to Cut Through Complexity

A unified repository for quality data helps manufacturers by putting all their information in one place. Dashboards simplify the way people can look at that data and enable a big-picture view of quality across complex manufacturing processes.

Quality improvement dashboards surface information that has been collected from multiple sources and synthesize it into simple visual models. They cut through the complexity and bring the most pressing issues to the forefront through customized reports and notifications.

Without dashboards, quality teams could easily become buried under enormous amounts of data, and decision-making could grind to a halt. Perhaps worse, leaders might not understand where their biggest problems are hidden, resulting in massively inefficient attempts to improve quality.

Quality dashboards ease data overload and improve:

  • Efficiency—When it’s easy to see the data that’s relevant, you can determine where to spend your time and resources, instead of wasting time and money wondering where to start.
  • Communication—When everyone has access to the same quality information, pulled from standardized data, it’s easier to streamline communication, create best practices, and keep everyone on the same page.
  • Collaboration—Visual models provide an easy-to-understand snapshot of performance and make it easier to share information and solicit feedback from multiple experts.

See Your Quality Data in Action

Do you want a clearer view of quality? See how InfinityQS software and quality dashboards make it easier to take action on your most important quality initiatives.

QualityControl_Dashboard

 

Tailor Quality Reporting by Role

InfinityQS quality improvement solutions centralize and standardize key quality information; dashboards enable that information to be dispersed quickly and consistently across the organization. With statistical process control (SPC)-driven dashboards, everyone uses the same data to inform their decision-making.

Users may need different levels of information based on their roles in the manufacturing process. InfinityQS dashboards can be tailored for different user types, so everyone gets the level of detail they need, without sacrificing the consistency that makes the data reliable.

Dashboards can be customized to support the needs of plant floor operators, managers, and executive users.

Give Plant Floor Personnel Real-Time Data

Plant floor operators need to act quickly and confidently to keep the manufacturing process running smoothly. They don’t have time to juggle spreadsheets or dig through extraneous data.

That’s why InfinityQS dashboards put everything plant floor operators, engineers, and supervisors need front and center. The most critical information is summarized into high-level tiles so supervisors can prioritize their efforts on the most critical quality concerns—or head off issues. Operators and engineers can receive notifications based on real-time SPC intelligence so they can respond swiftly to any process variations or missed data collections.

QualityMetrics_Dashboard

 

Help Managers Drill into the Details

Management teams need to be able to spot trends, investigate events, and uncover opportunities to improve quality. InfinityQS quality improvement dashboards can be configured for more analytical decision-making in addition to real-time views of the organization.

Managers can use quality dashboard tile and metatag features to drill down into specific key performance indicators (KPIs) across sites, products, and processes.

If needed, they can also view statistical process control (SPC) charts, plus box-and-whisker plots and Pareto charts. Because InfinityQS dashboards are fed by a centralized and standardized data repository, management teams can be confident in their analyses, take decisive actions, and share best practices across teams and locations.

QualityDashboards_Executive

 

Unite Quality Efforts Across the Enterprise

InfinityQS dashboards offer executive leaders the flexibility to see quality manufacturing processes in their entirety or at line-level detail.

With InfinityQS solutions, leaders can enter, view, and analyze quality data in real time and from anywhere, so they can stay in tune with critical manufacturing operations. Standardization across the enterprise makes it faster for executives to evaluate quality metrics by site, product, or process, and simple visual models enable intelligent analyses.

Executive reports are customizable and reusable, which helps leaders plot their organization’s progress over time and set data-driven goals for future initiatives. Dashboards also help executives cut through the clutter and quickly focus on sites or processes that need their attention—and prioritize the improvements that will have the biggest impact.

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What to Expect

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Quality Control Methods

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Quality Control Methods Can Uncover Opportunities

Before manufacturers can improve quality, they have to measure. Quality checks provide essential data that leaders need to make process improvement decisions. Quality monitoring and management is also required to verify that manufacturers are meeting regulatory requirements or customer specifications.

To gather all of the data they need to ensure quality standards are met, quality managers must juggle a variety of quality control methods. By the end of each day, they accumulate massive amounts of information. And then what?

Unfortunately, many quality managers lack time to do anything with their quality data beyond “checking the boxes.” That means they’re missing major opportunities.

By incorporating your proven quality control methods into a digital quality solution, you can access insights fast and resolve problems at lightning speed.
QualityControl_FloorChecks

A Solid Foundation: Statistical Process Control for Quality Improvement

A top quality manufacturing approach starts with statistical process control (SPC), the industry-standard approach to measure and control manufacturing quality. At a fundamental level, SPC entails continuous and consistent inspection and mapping of results to reveal variations.

Companies who use SPC to drive continuous improvement are able to:
  • Dramatically reduce waste and scrap
  • Lower operating costs
  • Minimize downtime

Real-time access to SPC quality data can change the way you approach quality. Rather than react to problems, you can prevent them.

Quality professionals strive to achieve these benefits by applying a wide range of quality control methods such as:

  • Specifications—Manufacturers set requirements that a product or service must meet.
  • In-Process Sampling—Either randomly or at timed intervals, sample units are pulled from the line for inspection, measured, and recorded.
  • Control Limits—Sample results are compared against established statistical boundaries. The measurements are used to determine whether processes are operating as expected or exhibiting unusual behaviors. Using proper control limits, one can detect even small deviations from the established norm.
  • Process Capability Indexing—Variations can be measured and compared to their specifications limits to quickly determine levels of expected fallout and visually see whether a problematic process is inherently not capable of meeting requirements, or if the fix is just a simple adjustment.
QualityControl_Dashboard

A Picture of Continuous Improvement

Process behaviors are brought to life using SPC control charts, which are graphical representations of a process’ output patterns compared to statistical limits. Control charts help quality leaders turn thousands of individual data points into an insightful story about quality. Because they provide an at-a-glance view of data, they may provide the first indication that quality is slipping, and they can guide in-depth investigations and analyses.

InfinityQS software is designed to intelligently build and display control charts so manufacturing leaders can solve quality problems quickly—and uncover new opportunities—without juggling spreadsheets or calling IT for support.

InfinityQS supports all the most commonly used SPC tools, such as:

Do You Know Where to Focus Your Time?

InfinityQS solutions give quality professionals unprecedented visibility into products, processes, and operations without the burden, time, and effort of building charts and reports manually. See how our control charts, dashboards, and alerts help leaders prioritize and speed up quality improvement efforts—and maximize results.

 

Improve Quality in Less Time

With traditional quality control tools, quality professionals are faced with too much to do and not enough time. Modern SPC-based quality management software can help manufacturers improve quality operations without draining their most valuable resource: time.

Leveraging SPC, InfinityQS solutions can:

  • Reduce complexity—Visual models such as control charts and dashboards simplify quality control. Issues that need immediate attention stand out, and you can connect quality issues to their root causes faster.
  • Accelerate results—With InfinityQS software, preventive or corrective actions can be taken in real time. Empowered team members can monitor quality control methods from nearly any device and initiate cost-saving measures without delay.
  • Take quality to the next level—With strong quality control methods in place, manufacturing teams can uncover key opportunities for improvement and build a strong culture around quality.

Ramp up is easy. InfinityQS software is designed specifically for manufacturing companies and comes with intuitive user interfaces and extensive self-help resources. Data collection methods are designed to fit seamlessly into your existing production processes—and never burden operators or slow down the line.

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What to Expect

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  • Explore which solutions best suit your needs
  • No-pressure conversation
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Xbar and Range (Xbar-R) Chart

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What are the Components of the Xbar and Range Chart?

The Xbar chart—the upper section in this statistical process control (SPC) chart—plots the average of individual values in a subgroup (i.e., the subgroup mean). The Range chart (R)—(the lower section in the chart— plots the difference (or range) between the maximum and minimum individual values within the subgroup.

Xbar-R Charts for a Single Characteristic

An Xbar-R chart is a quality control chart used to plot subgroup means and ranges of individual values from a single characteristic on a given part that were all produced on the same machine. A traditional Xbar-R chart is a single stream of data for a unique Part/Process/Test combination.

For example, this chart (taken from InfinityQS® ProFicient™ software) shows 20 subgroups. The highlighted section shows that both the average and range plot points for subgroup 8 are well within control limits. Judging from the control chart as a whole, this process is consistent (no plot points fall outside control limits) and only common cause variation is present.

Scroll down to learn how to use this chart.

Automate and Simplify Control Chart Analysis

See how easy it is to access actionable information from your SPC control charts.

When to Use the Xbar-R Chart

Use the Xbar-R chart when the sample size is between 2 and 9 (typically 3 or 5). This chart is often used when at least a few parts are made every hour and you can collect data at a reasonable cost.

The special use examples discussed for this chart all deal with sample sizes between 2 and 9.

Advantages and Disadvantages of Using the Xbar-R Chart

InfinityQS® software takes this chart technology to the next level by supporting multilevel Pareto charts—up to 10 levels deep.

Advantages

  • Easy to read and understand
  • Widely recognized; operates on principles that serve as the foundation for more advanced control charts
  • Separates variation in averages from variation in standard deviation

Disadvantages

  • Must use a separate chart for each characteristic
  • Only two values per subgroup are used to estimate the standard deviation for the range, regardless of sample size
  • Cannot be used to accurately indicate process variability for sample sizes greater than 9

Decision Tree

Use the following decision tree to determine whether the Xbar-R chart is the best choice.
Scroll down to see special use examples.

Special Uses

Today, control charts are a key tool for quality control and figure prominently in Lean manufacturing and Six Sigma efforts.

Target Xbar-R Chart

Target Xbar-R charts can help you identify changes in the average and range of averages of a characteristic. You can measure the characteristic across part numbers, but each part number must form a separate subgroup because target values change with the part number. Set the target values at the desired center, typically the center two-sided specifications.

  • Plot multiple parts, characteristics, or specs on the same chart, as long as variability is similar across all parts, characteristics, or specifications.
  • Plot data from gauges that are zeroed out on target values without needing to code or transform the data.
  • Assess statistical control for both the part (or characteristic) and the process.

Short Run Xbar-R Chart

Short run charts are used for short production runs. The short run Xbar-R chart can help you identify changes in the averages and range of averages of multiple characteristics, even those with different nominals, units of measure, or standard deviations.

  • Use one chart to detect variations across multiple process or product characteristics, even for parts that have different means, units of measure, or standard deviation.
  • Identify characteristics that should be prioritized for attention.
  • Easily separate process- and product-specific variations as well as variations that are caused by changes in a subgroup mean and those that are caused by changes in the standard deviation.

Group Xbar-R Chart

Group Xbar-R charts help you assess changes in averages and the range of averages across measurement subgroups for a characteristic.

  • Easily identify characteristics that need priority attention.
  • Easily separate process- and product-specific variations as well as variations that are caused by changes in a subgroup mean and those that are caused by changes in the standard deviation.
  • Track multiple characteristics on the same chart.

Group Target Xbar-R Chart

The group target Xbar-R chart provides information about changes in process averages and the range of averages across multiple measurement subgroups of similar characteristics that have a common process. Part numbers and engineering nominal values can differ across these characteristics.

  • Track multiple characteristics or similar characteristics with different averages on the same chart.
  • View both product and process characteristic variations.
  • See the difference between variations that are caused by changes in average and those caused by changes in the standard deviation.

Group Short Run Xbar-R Chart

When you need to evaluate changes in the process average and range of averages across multiple characteristics in a short run environment, use the group short run Xbar-R chart.

  • See the variations of multiple process or product characteristics on one chart, even within short production runs.
  • Analyze characteristics from multiple parts with different means, standard deviations, and units of measure.
  • Easily separate process- and product-specific variations as well as variations that are caused by changes in a subgroup mean and those that are caused by changes in the standard deviation, even in short run environments.

Group Short Run Xbar-R Chart Example

Simplify process monitoring by representing data for multiple parts and multiple characteristics on one chart.

How Do You Use Group Short Run Xbar-R Charts?

Group short run Xbar and range (Xbar-R) charts can help you evaluate changes in the process average and range of averages across multiple characteristics in a limited production run. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group short run Xbar-R chart works.

Figure 1. Two parts containing multiple key characteristics.

Table 1. Key characteristics with respective target values.

Case Description

A single lathe produces many different part numbers, each with many different key characteristics. The two parts shown in Figure 1 are examples. The manager of the machine shop wants to use only one chart for each lathe to monitor the process regardless of the part numbers or key characteristics being produced.

Bring SPC Charts Up to Speed

This example provides a deep dive into the manual calculations behind the group short run Xbar-R chart. InfinityQS® solutions—ProFicient™ and Enact®—automate chart creation and help you optimize processes faster.

LEARN MORE ABOUT MODERN SPC SOLUTIONS.

Sampling Strategy

The same chart must allow for different part numbers and different key characteristics. Because each characteristic may be unique with respect to its nominal, tolerance, and unit of measure, a group short run Xbar-R chart is selected. This chart will separate variation due to the lathe from variation unique to each part and characteristic.

The cycle time varies, but lot sizes are typically 20 to 100 parts. Cutting tools are replaced about every three hours. The data represent measurements taken every fifteenth part regardless of the part number (n = 3).

Data Collection Sheet

Table 2. Data collection sheet for the group short run Xbar-R chart lathe example. MAX and MIN plot points are shown in bold.

Group Short Run Xbar-R Chart

Figure 2. Group short run Xbar-R charts representing two parts and multiple characteristics.

Chart Interpretation

Group short run range chart: During the -101 part run, key characteristic width W appears in the MAX position all three times. There is a possibility of this happening by chance if all four keys are behaving randomly about their target values, but this may be an indicator of significantly greater variability in the W dimension as compared with others.

The L dimension appears in the MIN position five out of seven times. This likely represents a nonrandom pattern indicating less variability in the L dimension across both parts.

Group short run Xbar chart: The L characteristic on both the -101 and -27A appears in the MAX position six out of seven times. The chance of this occurring randomly is very small. This is most likely a nonrandom pattern that is related to the process itself. That is, regardless of the part number, the process tends to cut lengths on the high side.

During the manufacture of the -27A part, the rim of three plot points in the MIN position for dimension X may indicate the presence of a nonrandom pattern.

Recommendations

  • Operators and process engineers should try to identify why the lathe tends to cut all part lengths on the high side and why the W dimension on the -101 part displays more relative variation than the other three key characteristics. In addition, operators and engineers should try to isolate the reason why the L dimension varies less than other dimensions.
  • Watch the X dimension on the -27A part and subsequent part numbers. If the dimension continues to fall in the MIN position on the group short run Xbar chart, there should be an investigation for nonrandom patterns that relate to process-specific causes. If, however, the X dimension fails to fall into the MIN position for subsequent part numbers, the cause should be treated as product specific.

Estimating the Process Average

Estimates of the process average are calculated separately for each characteristic for each part on the group short run charts. This is illustrated in Calculation 1 using data from the H dimension on the -27A part.

Calculation 1. Estimate of the process average for characteristic H on part -27A.

Estimating Sigma

Estimates of sigma are also calculated separately for each characteristic on each part on the group short run charts. Continuing with characteristic H, sec Calculations 2 and 3.

Calculation 2. R calculation for characteristic H on part -27A.

Calculation 3. Estimate of the process standard deviation for characteristic H on part -27A.

Note: To ensure reliable estimates, k needs to be at least 20. In this example, k is only four. Therefore, the estimates shown here and in Table 3 are used only for illustration purposes.

Calculating Process Capability and Performance Ratios

Calculations 4, 5, and 6 show the process capability and performance calculations for characteristic H.

Calculation 4. Cp calculation for characteristic H.

Cpk-Formula-Upper-Calculation-image

Calculation 5. Cpk upper calculation for characteristic H.

Cpk-Formula-Lower-Calculation-image

Calculation 6. Cpk lower calculation for characteristic H.

Group Short Run Xbar-R Chart Advantages

  • Graphically illustrates the variation of multiple product or process characteristics on the same chart.
  • Characteristics from different parts with different means, different standard deviations, and different units of measure can be analyzed all on the same chart.
  • Separates variation due to changes in the average from variation due to changes in the standard deviation.
  • Separates variation due to the process from variation specific to a product characteristic.

 

Group Short Run Xbar-R Chart Disadvantages

  • No visibility of characteristics that fall between the MAX and MIN plot points.
  • Cannot detect certain out-of-control conditions because the group charts described here have no control limits.
  • Many calculations are required to code the data.

 

Additional Comments About the Case

  • Additional statistics and process capability and performance calculations for part characteristic L and X for part -27A are shown in Table 3.
  • Notice that characteristic L, while not capable, has a negative Cpku L value. This indicates that XL falls outside of the upper specification limit. In fact, the average falls more than 0.020 mm outside of the USL of 114.03 mm. This underscores the importance of reacting to characteristic L’s nonrandom pattern shown on the group short run Xbar chart in Figure 2.
  • Characteristic X has Cp and Cpk values that arc not only greater than one, but very close, numerically to one another. Therefore, characteristic X is capable and its Xx is almost perfectly centered on its engineering nominal value of 16.500 mm.

Table 3. Additional statistics and process capability and performance ratios for characteristics L and X from part -27A.

FOOTNOTE: 1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

Group Target Xbar-R Chart Example

Get visibility into process and part variability at a granular level.

How Do You Use Group Target Xbar-R Charts?

Group target Xbar-R charts provide information about changes in process averages and the range of averages across multiple measurement subgroups of similar characteristics that have a common process. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group target Xbar-R chart works.

Figure 1. Three sleeve-inside-diameter key characteristics.

Case Description

This sleeve contains three inside diameter key characteristics. They are all machined on the same lathe but with different tools. Each inside diameter is a different size. The customer requires stability of the lathe process as well as capability information from each inside diameter.

Bring SPC Charts Up to Speed

This example provides a deep dive into the manual calculations behind the group target Xbar-R chart. InfinityQS® solutions—ProFicient™ and Enact®—automate chart creation and help you optimize processes faster.
LEARN MORE ABOUT MODERN SPC SOLUTIONS.

Sampling Strategy

Visibility is required of both process and part variability. Because the same type of characteristic (sleeve diameters) with different targets is being measured at multiple locations on the same part, a group target Xbar-R chart is selected. This chart will highlight both variation in the lathe and variation in each of the three sleeves.

The cycle time required to manufacture a sleeve is three minutes. Cutting tools are replaced about every two hours. The subgroups represent measurements taken every hour from three consecutive sleeves.

Data Collection Sheet

Table 1. Group target Xbar-R chart data for three sleeve characteristics. MAX and MIN plot points are shown in bold.

Group Target Xbar-R Chart

Figure 2. Group target Xbar-R chart representing three different sized inside-sleeve diameters.

Chart Interpretation

Group target range chart: Either characteristic a or c shows up in the MAX position in every group. This suggests that these two locations have the largest standard deviation values. Location b appears in the MIN position in every group. This means that, of the three diameters being evaluated, location b has the least variability.

Note: The centerline on the group range chart is the average of all the ranges in the data collection sheet.

Group target Xbar chart: Diameter a dominates the MAX position. It consistently deviates from its target (to the high side) more than the other diameters. Location c dominates the MIN position. It consistently deviates from its target (to the low side) more than the other diameters. Diameter b falls in between. It deviates from its target value less than diameters a or c. This is characteristic of taper in the diameters. Also, notice that the MAX and MIN lines are somewhat parallel and seem to gradually trend upwards.

Note: The centerline on the group target Xbar chart is the average of all the coded Xbar plot points in the data collection sheet.

 

Recommendations

  • Operators should find out why the diameters on the ends (a and c) have larger standard deviations. One might evaluate the cutting tools, the way the sleeve is held when machined, part loading techniques, wall thicknesses at the different locations, coolant flow, or measurement problems.
  • People working in the process should try to eliminate the taper among the diameters. Change the process so that the a and c diameters fall closer to their targets.
  • The upward trend on the Xbar chart appears to be a predictable tool wear condition. One may consider performing a regression analysis to estimate when the cutting tools should be replaced.

Estimating the Process Average

If all of the key characteristics on the group target Xbar chart appeared to be behaving randomly, a single estimate of the process average could be used to estimate the process average for all locations. However, in this case, the group target Xbar chart does not exhibit random behavior.

Given this nonrandom behavior on the group target Xbar chart, estimates of the process average should be calculated separately for each characteristic on the group target chart. This is illustrated in Calculation 1 using data from diameter a.

Calculation 1. Estimate of the process average for diameter a.

Estimating Sigma

Estimates of sigma arc also calculated separately for each characteristic on the group chart. Continuing with diameter a, see Calculations 2 and 3.

Calculation 2. Calculation of R for use in estimating the process standard deviation for diameter a.

Calculation 3. The estimate of the process standard deviation for diameter a.

Note: To ensure reliable estimates, k needs to be at least 20. In this example, k is only nine. Therefore, the estimates here and in Table 2 are for illustration purposes only.

Calculating Process Capability and Performance Ratios

Calculations 4, 5, and 6 show the process capability and performance calculations for diameter a.

Calculation 4. Cp calculation for diameter a.

Cpk-upper-calculation-formula-img-2

Calculation 5. Cpk upper calculation for diameter a.

Cpk-lower-calculation-formula-img-3

Calculation 6. Cpk lower calculation for diameter a.

Group Target Xbar-R Chart Advantages

  • Simultaneously illustrates the variation of multiple product or process characteristics.
  • Similar characteristics with different averages can be analyzed on the same chart.
  • Separates variation due to changes in the average from variation due to changes in the standard deviation.
  • Multiple characteristics can be tracked on one chart.

 

Group Target Xbar-R Chart Disadvantages

  • No visibility of the characteristics that fall between the MAX and MIN plot points.
  • The use of negative numbers can be confusing.
  • Cannot detect certain nonrandom conditions because the group charts described here have no control limits.

 

Additional Comments About the Case

  • The remaining process statistics and process capability and performance ratios for diameters and are shown in Table 2.
  • Diameter a is not capable. Its average is greater than its target by almost 0.0007″.
  • Diameter b is capable although its average is more than 0.0002″ lower than its target.
  • Diameter c is not capable and its average is more than 0.0006″ lower than its target.

Table 2. Additional statistics and process capability and performance values for diameters b and c.

FOOTNOTE: 1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

Group Xbar-R Chart Example

Check uniformity of multiple key characteristics on a single chart.

How Do You Use Group Xbar-R Charts?

Group Xbar and range (Xbar-R) charts help you assess changes in averages and the range of averages across measurement subgroups for a characteristic. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group Xbar-R chart works.

Figure 1. Three OD key characteristics on a poppet.

Case Description

A poppet is manufactured on a screw machine. Rejection rates due to inconsistent ODs have been unacceptably high. Therefore, uniformity of the OD is designated as a key characteristic. To check the uniformity, three OD measurements arc taken on each poppet at locations ab, and c. Although the dimensions of the poppet could also be monitored using three separate Xbar-R charts—one for each dimension—quality assurance wants to monitor the diameter using only one chart. This is why the group Xbar-R chart is selected.

Bring SPC Charts Up to Speed

This example provides a deep dive into the manual calculations behind the group Xbar-R chart. InfinityQS® solutions—ProFicient™ and Enact®—automate chart creation and help you optimize processes faster.

 

LEARN MORE ABOUT MODERN SPC SOLUTIONS.

Sampling Strategy
Because the same characteristic is being measured at three different locations on the same part, a group Xbar-R chart is selected. Three poppets are measured every 15 minutes.

Data Collection Sheet

Table 1. Data collection sheet for the group Xbar-R chart. MAX and MIN plot points for each group are displayed in bold.

Group Xbar-R Chart

Figure 2. Group Xbar-R charts representing three ODs on the same part.

Chart Interpretation

Group range chart: Location c appears in the MAX position seven out of nine times. This strongly suggests that location c has the largest standard deviation. Location a appears eight out of nine times in the MIN position, therefore, location a most likely has the smallest standard deviation. The value of location b’s standard deviation falls somewhere between the value of the standard deviation of locations a and c.

Note: The centerline on the group range chart is the average of all 27 ranges found in Table 1.

Group Xbar chart: Locations a and b are in the MAX position six times and five times respectively. This sharing of the MAX position means that the average diameters of a and b behave similarly and they are always larger than location c, which appears nine out of nine times in the MIN position.

Note: The centerline on the group Xbar chart is the average of all 27 Xbar values found in Table 1.

 

Recommendations

  • These charts illustrate the lack of uniformity in the popper CD. The first recommendation is to change the process so that location c’s diameter increases enough to be in line with the size of the diameters at locations a and b. This might be done by reworking the cam or changing the program on the screw machine.
  • The large amount of variation at location c should also be addressed. To do this, operators might try a different way of positioning the work piece material in the holding fixture or find a different way to machine the dimension at location c.

Estimating the Process Average

Process average estimates should be performed separately for each characteristic or location on the group chart (see Calculation 1).

Calculation 1. Estimate of the process average for location a.

Estimating Sigma

Estimates of sigma are also calculated separately for each characteristic or location on the group chart. Continuing with location a, see Calculations 2 and 3.

Calculation 2. Calculation of R for location a.

Calculation 3. Estimated standard deviation for location a.

Note: To ensure reliable estimates, k needs to be at least 20. In this example, k is only nine. Therefore, these estimates and the ones found in Table 2 are shown only for illustration purposes.

 

Calculating Process Capability and Performance Ratios

Calculations 4, 5, and 6 show the process capability and performance calculations for location a.

Calculation 4. Cp calculation for location a.

Cpk-upper-calculation-sigma-img-2

Calculation 5. Cpk upper calculation for location a.

Cpk-lower-calculation-sigma-img-3

Calculation 6. Cpk lower calculation for location a.

Group Xbar-R Chart Advantages

  • Multiple characteristics can be tracked on one chart.
  • Pinpoints the characteristics that are most in need of attention.
  • Separates variation due to changes in the average from variation due to changes in the standard deviation.

 

Group Xbar-R Chart Disadvantages

  • No visibility of the characteristics that fall between the MAX and MIN plot points
  • Cannot detect certain out-of-control conditions because the group charts described here have no control limits

 

Additional Comments About the Case

The process capability and performance calculations for locations b and c are shown in Table 2.

Table 2. Additional summary statistics and process capability and performance ratios.

FOOTNOTE: 1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

Short Run Xbar-R Chart Example

Evaluate process control for short production runs and different part numbers.

How Do You Use Short Run Xbar-R Charts?

Short run X-bar and range (Xbar-R) charts can help you identify changes in the averages and range of averages of multiple characteristics—even those with different nominals, units of measure, or standard deviations—in limited production runs. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a short run Xbar-R chart works.

Figure 1. Example of sheet metal spring-back after hydroform operation.

Case Description

A hydroform is used to form angles in sheet metal. This is done by compressing a piece of sheer metal between a rubber pad and a form tool. When the metal is bent on the form tool, it springs back a few degrees when the pressure is released. To counteract the spring-back effect, the form tool angle exceeds the desired angle. In this case, the desired resultant sheet metal angles are 30°, 45°, and 90°. The average spring-back and standard deviations are different for each angle. The production foreman wants to use one control chart to monitor the spring-back behavior of all three types of angles. Table 1 shows the spring-back target values and specifications.

Table 1. Spring-back target values and specifications for three types of angles.

Note: The target X values are based on engineering nominal values and the target R values are based on historical quality records.

Bring SPC Charts Up to Speed

This example provides a deep dive into the manual calculations behind the short run Xbar-R chart. InfinityQS® solutions—ProFicient™ and Enact®—automate chart creation and help you optimize processes faster.

LEARN MORE ABOUT MODERN SPC SOLUTIONS.

Sampling Strategy

The hydroform machine is initially set up to bend 45° angles. Five consecutive spring-back measurements are taken every hour until the job is complete. Next, the machine is set up to run 30° angles and so on. Sampling continues in the same manner as before. All measurements are plotted on the same short run Xbar-R chart.

Data Collection Sheet

Table 2. Spring-back data including short run plot point calculations.

Short Run Xbar-R Chart

Figure 2. Spring-back short run Xbar-R control charts.

Chart Interpretation

Short run range chart: Three 30° plot points fall above the XJCL and are an indication that the variability for the 30° bends is greater than expected. The 45° plot points appear to be behaving randomly. The 90° plot points all fall below the centerline. Each pattern appears to be unique to each bend angle. There appear to be no visible patterns or trends that consistently appear across all bend angles collectively.

Short run Xbar chart: All 11 30° plot points fall above the centerline and five fall above the UCL. This indicates that the actual spring-back on 30° bends is greater than the established 8.2° target value. The 45° plot points appear to vary randomly about their target value.

The 90° plot points all fall below the centerline with one of them falling below the LCL. This indicates that the actual spring-back on 90° bends is less than the target X value of 1.3°. All plot point patterns appear unique to each bend angle. No trends are apparent across all bend angles collectively.

Recommendations

30º Bend Angles

Range plot points erratically jumping above the UCL generally indicate unstable short-term variation. This might be caused by a process change that happens to occur within a subgroup. To pinpoint the cause, a 100-percent sampling strategy with a sample size of one may need to be temporarily established.
The average spring-back is consistently greater than the established target X of 8.2°. Investigate why the spring-back rates are so much larger than the engineering target and improve the process’ ability to maintain a lesser spring-back.

45º Bend Angles

Both ranges and averages appear to behave with consistent variability. The control chart reveals no specific process control issues that need to be addressed with respect to this bend angle.

90º Bend Angles

There are only three plot points on the short run chart that represent the 90° bend angles being produced (subgroups 10, 11, and 20). However, two of the three plot points on the short run Xbar chart are very close to the LCL and one falls below. If all three subgroups were consecutive, the two-out-of-three zone analysis rule would be triggered. The user of the control chart should try to find an obvious reason for the low bend angle values. If historical 90° bend angle data revealed points that were consistently stable about the center line on the control chart, then an investigation of recent process or raw material changes might be considered.

Estimating the Process Average

Estimates of the process average should be calculated separately for each characteristic or part on short run Xbar-R charts. In this case, estimates of the process average should be calculated separately for each different spring-back angle. Calculation 1 shows the calculation for die overall average of the 30° spring-back measurements.

Calculation 1. Estimate of the process average for 30° spring-back angles.

Estimating Sigma

Estimates of sigma are also calculated separately for each characteristic or location represented on short run Xbar-R charts. In this case, estimates of the process standard deviation should be calculated for each different spring-back angle.

Calculation 2. Calculation of the average moving range for 30° spring back-angles (to be used in estimating the standard deviation).

Calculation 3. Estimate of the process standard deviation for the 30° spring-back angles.

Note: To ensure reliable estimates, k needs to be at least 20. In this example, k is only 11. Therefore, the estimates here and in Table 3 should be used only as references.

 

Calculating Process Capability and Performance Ratios

Calculation 4. Cp calculation for the 30° bend angle spring-back.

Cpk-Formula-Upper-Calculation-img-2

Calculation 5. Cpk upper calculation for the 30° bend angle spring-back.

Cpk-Formula-Lower-Calculation-img-3

Calculation 6. Cpk lower calculation for the 30° bend angle spring-back.

Short Run Xbar-R Chart Advantages

  • Graphically illustrates the variation of multiple product or process characteristics on the same chart.
  • Characteristics from different parts with different means, different standard deviations, and different units of measure can be analyzed on the same chart.
  • Pinpoints the characteristics that are most in need of attention.
  • Separates variation due to changes in average from variation due to changes in the standard deviation.
  • Separates process variation from product-specific variation.

 

Short Run Xbar-R Chart Disadvantages

  • The use of negative numbers and unitless ratios may be confusing at first.
  • X, R, and the estimate of sigma must be calculated separately for each characteristic on the chart.
  • Proper chart analysis requires knowledge of how target values were derived.

 

Additional Comments About the Case

The process capability and performance ratio calculations for the 45° and 90° bend angle spring-back are shown in Table 17.7.

Cp-Cpk-calculations-img

Table 3. Cp and Cpk calculations for 45° and 90° bend angle spring-back characteristics.

FOOTNOTE: 1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

Using the Target Xbar-R Chart: Example

See how a quality professional uses the target Xbar-R chart to ensure consistent process performance and meet specifications for different customers.

How Do You Use Target Xbar-R Charts?

Target Xbar and range (Xbar-R) charts can help you identify changes in the average and range of averages of a characteristic. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a target Xbar-R chart works.

igure 1. Relief valve with adjustable cracking pressure capabilities.

Case Description

Cracking pressure, the pressure at which the relief valve opens, is a key characteristic. The valve can be adjusted during assembly to crack at different pressures. Each customer has his or her own crack pressure requirements.

In this example, the target Xbar-R chart allows quality personnel to monitor the crack-pressure testing for three customers and compare whether the process remains consistently on target when the spec requirements change.

Bring SPC Charts Up to Speed

This example provides a deep dive into the manual calculations behind the target Xbar-R chart. InfinityQS® solutions—ProFicient™ and Enact®—automate chart creation and help you optimize processes faster.

LEARN MORE ABOUT MODERN SPC SOLUTIONS

Sampling Strategy

Cracking pressure is the only characteristic, but the requirements change with each order (see Table 1). Because the production volume is steady and the standard deviation is expected to be consistent across all cracking pressure settings, a target Xbar-R chart is used to monitor the process. Valves are 100 percent tested, but for charting purposes, the test results from three out of every 30 valves are used for analysis on control charts.

Table 1. Crack pressure requirements for three valve customers.

Data Collection Sheet

Table 2. Data collection sheet for relief valves.

Target Xbar-R Chart

Figure 2. Crack pressure target Xbar-R control chart.

Control Limit Calculations

Calculation 1. Calculations for the crack pressure target Xbar chart.

Calculation 2. Calculations for the crack pressure range chart.

Chart Interpretation

Range chart: No out-of-control plot points. There are no shifts, trends, or runs. It appears that the ranges are stable. This normal pattern supports the assumption that the process standard deviation is not affected when the valves are adjusted to different cracking pressures.

Target Xbar chart: Plot point comparisons to both the coded Xbar and the zero line must be made. Relative to the coded Xbar ( –0.94) none of the jobs is centered; this is caused mainly by customer C’s job being run well below its target of 180 psi. These plot points are pulling down the entire average, thus causing there to appear significantly long runs of plot points above the coded Xbar.

Relative to the zero line, the valve for customer A is centered on target, valves for customer B are a little on the high side of the target, and customer C’s valves are running consistently low.

Recommendations

If a characteristic is not centered on its target, either the process needs to be adjusted or the target needs to be changed.

Assuming the targets are desired values,

  • Customer A valves are centered on target; no adjustment needs to be made.
  • Customer B valves are a little on the high side. The benefit of centering the crack pressure on its target may not be worth the effort required if the Cp and Cpk values are high (greater than 1.3).
  • Customer C valves need to be adjusted about 5 psi higher. However, before changing the process, people attending to the process should verify the off-target values are not caused by a faulty measurement system.

 

Estimating the Process Average

The average difference from target is not the same for all three valve adjustments. So calculations for X need to be done separately for each of the three customer requirements. The following example focuses on customer A valves.

Calculation 3. Calculation for customer A’s average cracking pressure.

Note: To ensure reliable estimates, k should be about 20. In this example k is only nine. Therefore, the calculations on these pages and in the additional comments section are used only for illustration purposes.

 

Estimating Sigma

Because the range chart is in control across all three customer requirements, the estimate of sigma for all valves may be based upon the range chart’s centerline (see Calculation 4). If the range chart were not in control, separate, reliable R values would need to be calculated for each of the customer requirements.

Calculation 4. Estimating sigma using R.

Calculating Process Capability and Performance Ratios

Because the R chart is in control, the same sigma may be used for separately calculating all process capability and performance ratios for the cracking pressures. Following are the Cp and Cpk calculations for customer A valves.

Calculation 5. Cp calculation for customer A valves.

Calculation 6. Cpk upper calculation for customer A valves.

Calculation 7. Cpk lower calculation for customer A valves.

Target Xbar-R Chart Advantages

  • Multiple parts, specifications, or characteristics can be plotted on the same chart (provided they all exhibit similar variability).
  • Data from gauges that are zeroed out on their target values can be plotted directly on the target Xbar without further data coding or transformation.
  • Statistical control can be assessed for both the process and each unique part and/or characteristic being made.

 

Target Xbar-R Chart Disadvantages

  • Control limits are valid only when the Rs from each part on the chart are similar. When they are not similar, the suspect part(s) must be monitored on a separate chart, or the data must be collectively evaluated on a short run chart.
  • When interpreting the target Xbar chart, both the zero line and the coded Xbar must be taken into account. This accounts for some added complexity when interpreting the chart.

 

Additional Comments About the Case

  • The process capability and performance ratio calculations for the cracking pressure are shown in Table 3.
  • When valves A, B, or C are run again, the new data can be combined with prior data.

Table 3. Cp and Cpk calculations for valves B and C.

FOOTNOTE: 1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

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Individual X and Moving Range (IX-MR) Chart

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What is the Individual X and Moving Range Chart?

The IX-MR chart is used to monitor process stability using individual values and moving-ranges as plot points. The Individual X chart (the upper chart in this figure) illustrates an actual individual reading or measurement taken for quality control sampling purposes. The Moving Range chart (the lower chart in the figure) shows the absolute difference between two consecutive individual values.

IX-MR Charts for a Single Characteristic

This example chart (taken from InfinityQS® ProFicient™ software) represents several batches of resin—a homogeneous mixture. The chart shows plot points representing the percent solids in each batch. The highlighted plot point shows that for subgroup 16, the moving range plot point exceeds the upper control limit of 0.9.

Scroll down to learn how to use this chart.

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How to Use the IX-MR Chart

Use the Individual X-Moving Range (IX-MR) chart when your sample size is one (n=1).

By using this chart, you can spot variability that falls outside of what would be considered “normal”—indicating a special cause of variation and a need for investigation and possible process adjustment—for a characteristic, such as percent solids in a homogenous mixture. This is a good chart to use when sampling is expensive, time-consuming, or destructive, or when variation from consecutive samples are likely to indicate a measurement error rather than a product variation.

Advantages and Disadvantages of Using the IX-MR Chart

InfinityQS® software takes this chart technology to the next level by supporting multilevel Pareto charts—up to 10 levels deep.

Advantages

  • Easy to understand
  • Requires only 15 to 25 individual measurements to estimate control limits
  • Can plot data after obtaining each measurement
  • Requires minimal calculations

Disadvantages

  • Does not independently separate variation in average from variation in standard deviation
  • Not sensitive enough to quickly identify small changes in process average or standard deviation
  • For some special uses, target origins need to be known for optimal analysis

Decision Tree

Use the following decision tree to determine whether the IX-MR chart is the best choice.
Scroll down to see special use examples.

Special Uses

Today, control charts are a key tool for quality control and figure prominently in Lean manufacturing and Six Sigma efforts.

Target IX-MR Chart

Target charts show multiple characteristics that have different nominal or target values—for example, different specification limits or different tolerances—all on one chart.

In these charts, a zero point represents the target value of each characteristic. Like traditional IX-MR charts, target IX-MR charts help you spot variation in a characteristic. By displaying data on the IX chart as deviation from target, target charts help you understand process variation across multiple parts or batches with different specification limit target values.

  • Monitor the consistency of a characteristic common to different parts in the same part family.
  • Assess tool wear across multiple runs of different part numbers.

Short Run IX-MR Chart

Short run charts accomplish the same goal as target IX-MR charts, but are used for short production runs. These charts combine short run data sets to analyze process capabilities in limited production runs.

  • Detect characteristics that need priority attention.
  • Gain visibility into the difference between variations caused by the process and those that are limited to one product.

Group IX-MR Chart

Group charts display several parameters, characteristics, or process streams on one chart. With a group IX-MR chart, you can assess relative uniformity or consistency across multiple data streams. In the group IX-MR chart, individual measurements and moving ranges from multiple locations are combined into a group.

  • Clearly and distinctly illustrate the extremes or lack of uniformity in a data set group.
  • Clearly detect opportunities for improvement.

Group Target IX-MR Chart

As you might expect, the group target IX-MR chart provides the insight of both a group IX-MR chart and a target IX-MR chart. Use this chart to get statistically valid information from multiple part numbers or characteristics that share a common process.

  • Get better visibility into the process instead of into individual parts or test characteristics.
  • See the difference between variations that are caused by changes in average and those caused by changes in the standard deviation.

Group Short Run IX-MR Chart

When you need to evaluate changes in individual measurements across multiple characteristics in a short run environment, use the group short run IX-MR chart.

  • Gain visibility into variations caused by the process as opposed to those that are caused by a specific product, even within short production runs.

Group IX-MR Chart Example

Pinpoint product and process characteristics that are most in need of attention to ensure consistency.

How Do You Use Group IX-MR Charts?

Group individual X and moving range (IX-MR) charts display several parameters, characteristics, or process streams on one chart, enabling you to assess relative uniformity or consistency across multiple data streams. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group IX-MR chart works.

Figure 1. Arc width key characteristic shown with three measurement locations and upper and lower specifications.

Case Description

The arc shown in Figure 1 is a sheet metal stamping. It serves as a guide for a tractor throttle control. For the throttle assembly to function correctly, the arc width must be uniform and within specification. If the width is too large, the assembly binds, if it is too small, the assembly will not lock into position. To monitor arc width uniformity, measurements are taken at three locations, a, b, and c. The quality department wants to use a chart that will examine all three locations simultaneously.

Bring SPC Charts Up to Speed

This example provides a deep dive into the manual calculations behind the group IX-MR chart. InfinityQS® solutions—ProFicient™ and Enact®—automate chart creation and help you optimize processes faster.

Sampling Strategy

Because the same characteristic is being measured at three different locations on the part and there is an interest in evaluating them all on one chart, a group IX-MR chart is used.

Data Collection Sheet

Table 1. Group IX-MR chart data collection sheet. MAX and MIN plot points are shown in bold.

Plot Point Calculations

The Group IX Chart

No calculations are required for the group IX. The MAX and MIN plot points are picked from the individual measurements. For example, in group 1, the largest (MAX) arc width is 0.6813 at location a. The smallest (MIN) width is 0.6790 at location b.

The Group MR Chart

The moving range is calculated by taking the absolute difference between individual measurements at the same location from two consecutive groups. For example, location a in group 2 is 0.6813 and location a in group 3 is 0.6811, so the moving range between the two groups is 0.0002. The moving range at location a between groups 1 and 2 is 0.0000 because the arc width is 0.6813 in both groups for the a location. The same calculations are performed for locations b and c.
Note: There is no moving range for group 1 because no previous measurements exist.

Group IX-MR Chart Plot Points

Table 2. Group IX-MR chart plot point summary.

Group IX-MR Chart

Figure 2. Group IX-MR chart for arc widths.

Chart Interpretation

Group moving range chart: Location b appears in the MAX position six out of eight times. This suggests that location has the largest standard deviation of all three locations. Location a appears in the MIN position in five of the eight groups. This suggests that the variability at location a may be less than the other two locations.

Note: The centerline (MR = 0.00036) is the average of all the ranges from the data sheet, not just the average of the MAX and MIN ranges.

Group individual X Chart: Location a dominates the MAX position. This means that the arc width at location a is consistently wider than locations b or c. Locations b and c are both found in the MIN position. Even though location c is MIN more often, the raw data show that the individual values for locations b and c are very similar.

The distance between the MAX and MIN lines on the IX chart—0.0023 at plot point 1 and 0.0021 at plot point 9—are indicators of the amount of taper across the arc.

Note: The centerline (IX = 0.67997) is the average of all the individual measurements from all nine groups.

Recommendations

  • The consistently larger thickness at location a should be reduced to make the location less prone to binding.
  • The variability at location b might be decreased by modifying the tooling to make the arc more rigid at location b when stamping.

This example is typical of what is found in many products that have within-piece variation problems. The group chart helps to detect and highlight those consistently high and low values.

Estimating the Process Average

Process average estimates should be performed separately for each characteristic or location on the group chart.

Calculation 1. Estimate of the process average for location a.

Estimating Sigma

Estimates of sigma are also calculated separately for each characteristic or location on the group chart. Continuing with location a, see Calculation 2.

Estimating-Sigma-Value-image

Calculation 2. Estimate of the process standard deviation for location a.

Note: To ensure reliable estimates, k needs to be at least 20. In this example, k is nine. Therefore, the estimates found here are used only for illustration purposes.

Calculating Process Capability and Performance Ratios

Calculations 3 through 5 show the process capability and performance calculations for location a.

Calculation 3. Cp for location a.

Cpk-upper-calculation-formula-2

Calculation 4. Cpk upper for location a.

Cpk-lower-calculation-formula-3

Calculation 5. Cpk lower for location a.

Group IX-MR Chart Advantages

  • Graphically illustrates the variation of multiple product or process characteristics simultaneously and relative to each other
  • Quickly pinpoints the characteristics that are most in need of attention

Group IX-MR Chart Disadvantages

  • Not as sensitive to changes in the process average as the group Xbar-R chart
  • No visibility of the characteristics that fall between the MAX and MIN plot points
  • Cannot detect certain out-of-control conditions because the group charts shown here have no control limits

Additional Comments About the Case

Table 3. Process capability and performance calculations for locations b and c.

FOOTNOTE: 1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

Group Short Run IX-MR Chart Example

Graphically illustrate variation in processes, products, and characteristics on one chart.

How Do You Use Group Short Run IX-MR Charts?

Group short run individual X and moving range (IX-MR) charts can help you evaluate changes in individual measurements across multiple characteristics in a short run environment. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group short run IX-MR chart works.

Figure 1. Several parameters are monitored for each batch of compounded adhesive solution.

Case Description

The same mixing equipment is used to mix several different types of adhesive compounds. Each compound has its own unique set of functional test requirements. In this example, three compounds are examined: compound A, B, and C. The test requirements for each are listed in Table 1.

Table 1. Test requirements for compounds A, B, and C.

Bring SPC Charts Up to Speed

This example provides a deep dive into the manual calculations behind the group short run IX-MR chart. InfinityQS® solutions—ProFicient™ and Enact®—automate chart creation and help you optimize processes faster.

Sampling Strategy

The test characteristics, specifications, and units of measure are different for each compound, and only one measurement of each characteristic is gathered from each batch. Therefore, a group short run IX-MR chart is selected for use. Target values are established for each characteristic from each compound. The target IX values are set at the engineering nominal, but the target MR values were derived from quality assurance records.

Target Values

Table 2. Target values for compounds A, B, and C.

Data Collection Sheet

Table 3. Group short run IX-MR chart data collection sheet. MAX and MIN plot points are shown in bold.

Group Short Run IX-MR Chart

Figure 2. Group short run IX-MR chart for three different compounded adhesive solutions.

Chart Interpretation

Group short run MR chart: There is a run of four consecutive hardness (H) plot points in the MAX position from compound B. This indicates that there is significantly more variation in the hardness characteristic than others.

Also, the first 10 MIN plot points are all chemical concentrations. This indicates that the chemical concentration characteristics exhibit the lowest variability of the characteristics being evaluated regardless of the compound.

Group short run Ichart: All but one of the MAX plot points from compounds A and B represent chemical concentrations. This means that the chemical concentrations are higher on average than their targets.

All of the MIN plot points for compound B represent the hardness characteristic (H). This run indicates that the average hardness is less than its target.

The set time (t) from compound A is in the MIN position four out of five times. This may indicate that the set time is generally quicker than its target time of 17.5 minutes.

Lastly, the reactant temperature from compound C is consistently in the MIN position indicating lower than target temperatures.

Recommendations

  • The MIN plot point run of chemical concentrations on the moving range chart appears to be significant. It indicates that the standard deviations are consistently less than expected by the established target MR. Therefore, identify the cause for this improvement and update the target values.
  • The MAX plot point run of chemical concentrations on the IX chart appears to be significant. The actual concentrations are consistently higher than expected by the target IX. Therefore, identify the cause(s) for these high concentrations and bring them closer to target. However, if the concentration levels were intentionally run high, the target IX values should be updated to reflect the desired concentration levels. The hardness (if) of compound B found on the group short run IX chart is consistently less than its target IX. Therefore, identify the cause and change the process to bring the hardness closer to target.
  • The set time for compound A is a little faster than its target value. If this is an improvement, update the target.
  • The reactant temperature (T) of compound C on the group short run IX chart is consistently less than its target value. Process personnel should attempt to do what is necessary to bring the temperature back up to target or determine if the present temperature level is desirable. If it is desirable, then the target temperature value should be updated.

Estimating the Process Average

Estimates of the process average are calculated separately for each characteristic of each compound on the short run group chart. This is illustrated in Calculation 1 using the percent solids (S) from compound C.

Calculation 1. Estimate of the process average percent solids content(s) from compound C.

Estimating Sigma

In estimating sigma, calculations must be performed separately for each characteristic of each compound on the group short run chart. Notice, however, that no moving ranges have been calculated—only coded MR values are shown in Table 3.

MR values should be calculated using consecutive IX values just as is done with IX-MR charts. So, in Calculations 2 and 3 and in Table 4, standard MR values have been used in calculating estimates of sigma.

Calculation 2. Average moving range for percent solids content from compound C to be used in the estimate of process standard deviation in Calculation 3.

Calculation 3. Estimate of the process standard deviation for percent solids content from compound C.

Note: To ensure reliable estimates of both the process average and process standard deviation, k needs to be at least 20. In this example, k is only six. Therefore, the estimates here and in Table 4 are shown only for illustration purposes.

Calculating Process Capability and Performance Ratios

Calculation 4. Cp for percent solids content from compound C.

Cpk-upper-for-percent-solids-content-2

Calculation 5. Cpk upper for percent solids content from compound C.

Cpk-lower-for-percent-solids-content-3

Calculation 6. Cpk lower for percent solids content from compound C.

Group Short Run IX-MR Chart Advantages

  • Graphically illustrates the variation of multiple products and their characteristics simultaneously on the same chart.
  • Characteristics from different parts with different means, different standard deviations, and different units of measure can all be analyzed on the same chart.
  • Illustrates variation of the process and variation of the specific products.

Group Short Run IX-MR Chart Disadvantages

  • No visibility of the characteristics that fall between the MAX and MIN plot points.
  • IX, MR, and estimates of sigma must be calculated separately for each characteristic on the chart.
  • Analysis and recommendations can be tricky if target origins are not known.

Additional Comments About the Case

Additional statistics and process capability and performance calculations for compound C’s chemical 1, clarity, and reactant temperature are shown in Table 4.

The largest cause for compound C’s rejections is due to reactant temperature failures. Based on the Cpkl of –0.06, more than 50 percent of the batches will fall below the lower specification. With failures this large, one of two actions ought to be considered.

  1. Change the process to ensure a higher average reactant temperature. This might be a good time to perform a designed experiment to help determine what to change in the process.
  2. Reexamine the need for the LSL to remain at 85°. If it can be lowered without compromising adhesive performance, change the specification and allow the average temperature to remain at its current level of 84.91°.

Table 4. Process capability and performance calculations for compound C’s chemical 1, clarity, and reactant temperature.

FOOTNOTE: 1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

Group Target IX-MR Chart Example

Spot sources of variation unique to a process, product, and characteristic—on a single chart.

How Do You Use Group Target IX-MR Charts?

Group target individual X and moving range (IX-MR) charts combine the insights of a group IX-MR chart and a target IX-MR chart to provide statistically valid information from multiple part numbers or characteristics that have a common process. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group target IX-MR chart works.

Figure 1. Three generic key characteristics for the seat product line.

Case Description

Three generic key characteristics are monitored on several different seat products. All seats share three common key characteristics and tolerances.

  • Key a, inside diameter (nominal + 0.001)
  • Key b, length (nominal + 0.001)
  • Key c, OD (nominal + 0.005)

Seats are manufactured in many different sizes. In this example, three different seat product series (the -400, -800, and -900) will be evaluated. Each of the three seat series is machined on the same lathe but with different tools. Each characteristic is a different size, but the standard deviations are expected to be similar. The shop supervisor wants to analyze the stability of all three key characteristics, regardless of series number, on one chart (see Table 1).

Table 1. Key target values for the three different seat product series.

Bring SPC Charts Up to Speed

This example provides a deep dive into the manual calculations behind the group target IX-MR chart. InfinityQS® solutions—ProFicient™ and Enact®—automate chart creation and help you optimize processes faster.

Sampling Strategy

Given low production volume and multiple characteristics of different sizes, a group target IX-MR chart is selected. This chart will help operators evaluate the variation due to the lathe and variation specific to each characteristic/product series combination. The data in Table 2 represent measurements taken at the lathe every hour in subgroup sizes of one.

Data Collection Sheet

Table 2. Group target IX-MR data and plot points (shown in bold) for the three seat product line characteristics.

Plot Point Calculation

Group MR chart: Moving range values are calculated by taking the absolute value between individual measurements from consecutive groups for the same location. For example, location a in group 2 is 0.4455 and location a in group 1 is 0.4448, so the MR between the two groups is 10.4455 — 0.44481 = 0.0007. MAX and MIN values within each group are used as plot points.

Note: Because the same part series was not evaluated in any previous group, no MR values exist for groups 1, 4, or 7.

Group Target IX-MR Chart

Figure 2. Group target IX-MR chart used to evaluate three different key characteristics from three similar parts.

Chart Interpretation

Note: There are only three groups per part series in this example, therefore, any plot point patterns unique to a part series should be considered only when more data become available.

Group MR chart: MAX and MIN plot points from consecutive groups appear to be descending over time. This could be the result of either

  1. The standard deviation getting smaller over time regardless of part number
  2. The -400 series parts exhibiting more variability than either the -800 or -900 series seats

With more data, this initial observation could be confirmed or rejected.

Note: The centerline on the group moving range chart is the average of all the moving ranges in the data set.

Group target IX chart: Key characteristic c appears in the MAX position six out of nine times. Because this is true across all three part series, it may indicate a condition inherent to the process instead of one specific to a part series. Operators speculate it has to do with the lathe’s apparent difficulty in machining the ODs. There might be something unique about why the lathe tends to run ODs a little higher than specified. Or the problem may be attributed to the programmer having written the program to intentionally manufacture the diameters on the high side. Additional investigation will be required to pinpoint the reason for this nonrandom pattern.

Note: The centerline on the group target IX chart is the average of all the coded IX plot points in the data set.

Recommendations

  • As more data are collected, the operator should pay close attention to key characteristic c (the ODs). Look for reasons why the diameters on all part series might be a little high.
  • Look to see if the moving range plot points continue to decrease over time. It is possible that the -400 series key characteristics have larger standard deviations than the -800 or -900 series key characteristics. (The -800 and -900 series are larger parts, which could explain their smaller standard deviations.)

Estimating the Process Average

If all the part series and their characteristics on the IX chart appear to be behaving randomly, a single average of all coded individual values could be used to estimate the overall process average. However, because this was not the case for the seat products here, process averages will need to be estimated for each seat characteristic across all part series. This is done by calculating a coded IX value for each characteristic for all part series. An example for characteristic a is shown in Calculation 1.

Calculation 1. Estimate of the process average for key characteristic a.

Estimating Sigma

Estimates of sigma are also calculated separately for each characteristic on the group chart. Continuing with key characteristic a, see Calculations 2 and 3.

Group-Target-IX-MR-Estimating-Sigma-image

Calculation 2. Calculation of MR for key characteristic a across all seat series.

Group-Target-IX-MR-Estimating-Sigma-2-image

Calculation 3. Estimate of the process standard deviation for key characteristic a.

Note: To ensure reliable estimates, the number of groups should be at least 20. In this example, the number of groups is only 9. Therefore, these estimates and those found in Table 3 are shown only for illustration purposes.

Calculating Process Capability and Performance Ratios

These ratios are calculated using coded data. The coded target for each characteristic is zero. Calculations for key characteristic a across all three-part series are shown in Calculations 4, 5, and 6.

Calculation 4. Cp calculation for seat key characteristic a.

Calculation 5. Cpk upper calculation for seat key characteristic a.

Cpk-upper-calculation-image

Calculation 6. Cpk lower calculation for seat key characteristic a.

Group Target IX-MR Chart Advantages

  • Graphically illustrates the variation of multiple products and their characteristics simultaneously on the same chart
  • Separates sources of variation unique to the process, unique to the product, and unique to a characteristic on a single chart
  • Separates variation due to changes in the average from variation due to changes in the standard deviation

Group Target IX-MR Chart Disadvantages

  • No visibility of the characteristics that fall between the MAX and MIN plot points
  • The use of negative numbers can be confusing
  • Cannot detect certain out-of-control conditions because the group charts described here have no control limits

Additional Comments About the Case

Additional statistics and process capability and performance values for key characteristics b and c are shown in Table 3.

Table 3. Additional statistics and process capability and performance values for key characteristics b and c.

FOOTNOTE: 1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

Short Run IX-MR Chart Example

Assess process control for short production runs between different part numbers.

Short Run IX-MR Charts

Short run individual X and moving range (IX-MR) charts combine short run data sets to analyze process capabilities in limited production runs. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a short run IX-MR chart works.

Figure 1. Three fire extinguishing bottles, each with different burst pressure requirements.

Case Description

A certain manufacturer of aerospace fire extinguishing bottles performs destructive testing on each batch of bottles. The test involves pressurizing the bottle until it bursts. Burst pressure is the key characteristic. Each bottle’s burst requirements are different. Also, since each bottle type can be made of different materials with different wall thickness, burst pressure variability changes with each bottle type. For these reasons, a short run IX-MR chart is selected to monitor all data from the burst test. All target values were obtained from past control charts.

Table 1. Target values and minimum specification limit for all three bottle types.

Bring SPC Charts Up to Speed

This example provides a deep dive into the manual calculations behind the short run IX-MR chart. InfinityQS® solutions—ProFicient™ and Enact®—automate chart creation and help you optimize processes faster.

Sampling Strategy

Since burst testing is destructive, only one bottle from each lot is tested—typically the first piece. However, results from all burst tests are recorded on the same control chart. Tests are immediately performed as first-piece bottles become available. One test stand supports the entire manufacturing operation. Bottle types can change for each test.

Data Collection Sheet

Table 2. Burst test data including plot point calculations for the short run IX-MR chart.

Note: The MR and coded MR values found in Table 2 are calculated using previous data points from the same bottle type. For example, the coded MR value of 0.49 in subgroup 16 is the result of taking the absolute difference between the coded IX values in subgroups 13 and 16: |1.06 — 1.55| = 0.49.

Short Run IX-MR Chart

Figure 2. Bottle burst test data short run IX-MR control chart.

Chart Interpretation

Short run MR chart: Because there are no non-random patterns or points outside control limits, the variability in burst pressure is consistent across all three bottle types.
Short run IX chart: The individual plot points appear to be stable with no non-random patterns occurring.

Recommendation

Because both charts are in control, the target values (obtained from past control charts) are still appropriate for the current data. Continue maintaining the control chart with no changes in target values.

Estimating the Process Average

Estimates of the process average should be calculated separately for each characteristic or part on the short run IX and MR chart. In this case, estimates of the process average should be calculated separately for each bottle type. This is illustrated with bottle type A in Calculation 1.

Calculation 1. Estimate of average burst pressure for bottle type A.

Estimating Sigma

Estimates of sigma are also calculated separately for each characteristic or location represented on short run IX-MR charts. In this case, estimates of the standard deviation should be calculated for each bottle type. The calculation of MR for bottle type A is found in Calculation 2.

Calculation 2. Calculation of the average moving range for bottle type A (to be used in estimating its standard deviation).

Calculation 3. Estimate of the process standard deviation for bottle type A.

Note: To ensure reliable estimates, k needs to be at least 20. For bottle type A, k is only 9. Therefore, the estimates here and in Table 3 are used for illustration purposes only.

Calculating Process Capability and Performance Ratios

Recall that the minimum specification for bottle type A burst pressure is 1070. Because there is only a single minimum burst specification, Cp and Cpk upper are not calculated.

Cpk-lower-calculation-image

Calculation 4. Cpk lower calculation for bottle type A burst pressure.

Short Run IX-MR Chart Advantages

  • Graphically illustrates the variation of multiple product or process characteristics on the same chart.
  • Can chart process parameters that have changing target values. Characteristics from different parts with different means, different standard deviations, and different units of measure can be analyzed on the same chart.
  • Pinpoints the characteristics that are in need of the most attention.
  • Separates variation due to the process from variation that is product specific.

Short Run IX-MR Chart Disadvantages

  • The MR chart is dependent upon consecutive IX chart plot points.
  • IX, MR, and estimates of sigma must be calculated separately for each characteristic on the chart.

Additional Comments About the Case

  • The case study shown here displayed three bottle types. In the actual situation, there were 22 different bottle types being monitored on the same short run IX-MR chart.
  • Process capability and performance calculations for the remaining bottle types are shown in Table 3.

Table 3. Additional summary statistics and process capability and performance ratios for remaining bottle types.

FOOTNOTE: 1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

Target IX-MR Chart Example

Evaluate process control for part numbers with different target values.

How Do You Use Target IX-MR Charts?

Target charts show multiple characteristics that have different nominal or target values, with a zero point representing the target value of each characteristic. Target individual X and moving range (IX-MR) charts enable you to spot variation in a characteristic and plot several characteristics in the same chart. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a target IX-MR chart works.

Figure 1. Target percent solids from five different paint specifications.

Case Description

Solids content in paint is a key characteristic. To obtain a measure of solids content, a paint sample of known weight is taken from a mixing tank—one sample per paint batch. The sample is baked in an oven until only solids remain. The remaining solids are weighed and a percent solids is calculated. In this example, a mixing tank is used to produce five different types of paint: A, B, C, D, and E. Each paint type requires a different percent solids content. Long production runs rarely occur with any one paint. The production manager is monitoring the solids content from all five paints on the same SPC chart.

Bring SPC Charts Up to Speed

This example provides a deep dive into the manual calculations behind the target IX-MR chart. InfinityQS® solutions—ProFicient™ and Enact®—automate chart creation and help you optimize processes faster.

Sampling Strategy

A target IX-MR chart is used to monitor this process because

  1. Only one characteristic is being controlled (solids content).
  2. One measurement is representative of each batch.
  3. The user prefers to construct a single chart to track multiple paint specs.

Data Collection Sheet

Table 1. Data collection sheet for constructing target IX-MR chart.

Target IX-MR Chart

Figure 2. Percent solids target IX-MR chart.

Calculations for the MR Chart

Calculation 1. Calculations for MR chart.

MR Chart Interpretation and Recalculation

An upward spike occurs on the MR chart when the new supplier’s products begin to be used. Because the MR chart is out of control, this means that the value of MR is unreliable and cannot be used to calculate control limits for the target IX chart. This is why no control limits were placed on the target IX chart in Figure 2.
After removing the out-of-control plot point (subgroup number 14) from the MR chart, the MR was recalculated using the remaining 18 MR values (see Calculation 2).

Calculation 2. Revised MR chart calculations after removing subgroup number 14.

Note that all of the remaining moving range values fall within the new MR chart control limits (see Figure 3). There appears to be no indication of assignable causes of variation. Given this situation, it is now appropriate to complete the control chart calculations for the target IX chart.

Figure 3. Target IX-MR chart with revised control limits. Subgroup number 14 has been removed from calculations for the MR chart.

Calculations for the Target IX Chart

Calculation 3. Calculations for the percent solids target IX chart.

Target IX Chart Interpretation

It appears that, after the supplier change, the percent solids contents increased across paints A, B, and C. The run above the centerline between plot points 14 and 20 was determined to be the result of changing the supplier. The run below the centerline between points 4 and 9 is, in part, due to the upward shift in the centerline between points 14 and 20.

Note: When analyzing target charts, also look for patterns unique to each characteristic represented on the chart. For example, look to see if all of paint A plot points were above or below the centerline or trending upward or downward. In this example, all paint B plot points are above the centerline, but there are only two plot points. This does not qualify as an assignable cause. However, if eight or more plot points from the same paint were above the centerline, it would indicate an out-of-control condition unique to that paint. This would be true regardless of how many different paints were manufactured between those points.

Recommendation

Supplier changes should not be introduced into the line without first knowing how the change will affect the producibility and/or the finished product. If the effects are known in advance, prior adjustments can possibly be made without affecting the production line. In many cases, the costs associated with changing suppliers exceed the benefits of a lower price.

Estimating the Process Average

The coded IX on the control chart (–0.02 percent) has been upwardly influenced because of the supplier change assignable cause. Because of the presence of an assignable cause, the overall average of –0.02 percent is not a reliable estimate of the centering of the process.

To accurately estimate the overall process average, we will evaluate only the data from the old supplier (the first 13 subgroups). This data by itself proved to be in control on a separate target IX-MR chart (not shown here).

Calculation 4. Estimate of the process average based upon old supplier data (first 13 subgroups).

The coded IX from Calculation 4 shows that, on average, each old supplier batch of paint is approximately 0.15 percent below targets. If enough data were gathered from the new supplier data, it might be interesting to evaluate the old supplier’s coded IX with the new supplier’s IX.

Estimating Sigma

The MR chart for the first 13 subgroups (not shown) proved to be in control. The calculation for MR is shown in Calculation 5.

Calculation 5. Average moving range calculation from first 13 subgroups.

Estimating-Sigma-MR-Chart-2

Calculation 6. Estimating sigma using MR from Calculation 5.

Note that the first 13 subgroups represent only old supplier data. Therefore, the sigma found in Calculation 6 can be thought of as the estimated standard deviation for the old supplier. Notice, though, that the first 13 subgroups also are representative of process performance from paint specs A, D, and E. No data representing paint specs B or C are found. Therefore, paint specs A, D, and E will be used in calculating Cp and Cpk values. There will be no calculation of Cp or Cpk values for paint specs B or C.

Calculating Process Capability and Performance Ratios

Capability ratios will be calculated for each paint specification found in the first 13 subgroups. Because the MR chart is in control, the same sigma may be used in calculating process capability and performance ratios for paint specifications A, D, and E. The Cp calculation for paint specification A (assuming the old supplier’s materials are used) is found in Calculation 7.

Calculation 7. Process capability ratio for paint spec A using old supplier data.

In order to calculate CpkA, the process average must first be estimated for paint spec A. The estimate of the paint spec A process average is given in Calculation 8.

Calculation 8. Estimate of the process average for paint spec A.

Cpk-upper-calculation-3

Calculation 9. Cpk upper calculation for paint spec A.

Cpk-lower-calculation-4

Calculation 10. Cpk lower calculation for paint spec A.

Because the Cp value is greater than 1, the process is more than capable of producing almost 100 percent acceptable output. Because the Cpk value is smaller than the Cp value, it means that the process is a little off center, but because the Cpk value is larger than 1, the process is performing to specifications.
The Cp and Cpk ratios for paint specs D and E can be found in Table 2.

Note: To ensure reliable estimates of sigma and the process average, one needs about 20 data points. Therefore, the calculations on these pages and those in Table 2 are used for illustration purposes only.

Target IX-MR Chart Advantages

  • Multiple parts, specifications, or characteristics can be plotted on the same chart (provided they all have similar variability as exhibited by an in-control MR chart).
  • Cp and Cpk can be calculated for each characteristic on the chart.
  • Statistical control can be assessed for both the process and each unique part and/or characteristic on the chart.

Target IX-MR Chart Disadvantages

  • When interpreting the target IX chart, both the zero line and the coded X must be taken into account.
  • The MR plot points are dependent on the IX plot points. In other words, changes in the MR chart are directly related to changes from one individual measurement to the next.
  • Variation in the individual measurements could be caused by a shift in the average or the inherent standard deviation of the process; however, the IX-MR charts cannot efficiently separate the effects of the two.
  • Reliable control limits require the distribution of the individual measurements to be approximately normal.
  • The target IX-MR chart is not as sensitive to changes in the process average or standard deviation as would be a target Xbar-R chart.

Additional Comments About the Case

Cp and Cpk for paint specifications D and E are shown in Table 2.

Cp-and-Cpk-values-for-paint-D-and-E-image

Table 2. Cp and Cpk values for paint specifications D and E.

FOOTNOTE: 1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

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