Mitigate Risk

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Prioritize Quality and Process Optimization to Protect Your Brand

InfinityQS® solutions use proven statistical process control (SPC) methodology to help you prevent problems—and the associated risks.

Boost ROI
From giving you the insight you need to monitor supplier quality to improving traceability and streamlining audits, InfinityQS solutions provide unbeatable ROI.

Protect brand equity
Consistency is a hallmark of brand equity. How can you ensure that customers get the same high-quality product from any manufacturing site, at any time? How can you detect potential quality problems as quickly as possible—or better yet, spot the warning signs and prevent the problems? InfinityQS solutions provide targeted yet extensive data collection and capabilities, automated alerts, and aggregated access to historical data so that you can produce a consistently excellent product that meets brand expectations.

Reduce customer complaints
Your customers demand high quality, reliable products. You need proven, efficient quality control methods to meet those demands. One faulty process can set back both production and customer loyalty. With InfinityQS, you get solutions that help you respond to customer needs—quickly, flexibly, and consistently.

Minimize recalls
Product recalls are costly, not just in lost time and wasted materials but also in the potential loss of customer confidence and brand reputation. InfinityQS gives you the insight you need to reduce defect levels, automate policy and procedure enforcement, and reduce scrap and rework—all of which can help to prevent the dreaded recall.

Measurable Results

Hundreds of InfinityQS clients responded to a survey we conducted, documenting savings in key metrics including scrap, rework, defects, cycle time, overtime, warranty claims, MRB/sorting, holds, escapes, data collection, reporting and recalls.

The average results are as follows:

  • 12.7% Weekly Scrap Reduction
  • 14.3% Man-hour Rework Reduction
  • 14.1% Overtime Reduction
  • 12.9% Defect Cost Reduction
  • 13.6% Cycle Time Reduction
  • 14.1% Warranty Claim Reduction
  • 11.5% MRB/Sorting Reduction
  • 12.5% Holds Reduction
  • 10.7% Escapes Reduction
  • 14.4% Data Collection Time Reduction
  • 17.1% Report Time Reduction
Case Study

Elevating Quality to the Top Floor

Easy to start. Easy to expand.

Enact empowers you to quickly realize the benefits of digital data collection and analysis. Start today with:

  • Five Enact licenses: add more as needed
  • Quick Setup wizard: your guide to configuring data collections
  • Video tutorials and easy-to-use help: available in our Guided Learning Center
  • Flexible expansion: reconfigure your licenses, add licenses, integrate with other manufacturing systems, and move to automated data collection—at any time

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Ensure Product & Quality Compliance

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Minimize Production Costs, Quickly Detect Issues, and Optimize Your Product Quality

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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.

Meet Lean and Six Sigma requirements
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.

Simplify audits
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.

Comply with regulations
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.

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

Case Study

Electrical Devices

Easy to start. Easy to expand.

Enact empowers you to quickly realize the benefits of digital data collection and analysis. Start today with:

  • Five Enact licenses: add more as needed
  • Quick Setup wizard: your guide to configuring data collections
  • Video tutorials and easy-to-use help: available in our Guided Learning Center
  • Flexible expansion: reconfigure your licenses, add licenses, integrate with other manufacturing systems, and move to automated data collection—at any time

Request a Demo

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.

Automate and Simplify Control Chart Analysis

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

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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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.
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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

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  • Explore which solutions best suit your needs
  • No-pressure conversation
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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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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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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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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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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.

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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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