Quality Dashboards

Deliver the right data to the right people to improve quality.

 

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.

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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.

Speak to a InfinityQS Expert

What to Expect

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

Quality Control Methods

Use quality data more effectively to work smarter and faster.

 

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.

 

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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.

Speak to a InfinityQS Expert

What to Expect

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

Xbar and Range (Xbar-R) Chart

Learn how to use this combined view to track variation across across a single characteristic—and pinpoint issues at a glance.

What are the Components of the Xbar and Range Chart?

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

Xbar-R Charts for a Single Characteristic

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

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

Scroll down to learn how to use this chart.

Automate and Simplify Control Chart Analysis

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

When to Use the Xbar-R Chart

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

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

Advantages and Disadvantages of Using the Xbar-R Chart

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

Advantages

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

Disadvantages

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

Decision Tree

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

Special Uses

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

Target Xbar-R Chart

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

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

Short Run Xbar-R Chart

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

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

Group Xbar-R Chart

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

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

Group Target Xbar-R Chart

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

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

Group Short Run Xbar-R Chart

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

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

Group Short Run Xbar-R Chart Example

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

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

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

Figure 1. Two parts containing multiple key characteristics.

Table 1. Key characteristics with respective target values.

Case Description

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

Bring SPC Charts Up to Speed

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

LEARN MORE ABOUT MODERN SPC SOLUTIONS.

Sampling Strategy

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

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

Data Collection Sheet

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

Group Short Run Xbar-R Chart

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

Chart Interpretation

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

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

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

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

Recommendations

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

Estimating the Process Average

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

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

Estimating Sigma

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

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

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

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

Calculating Process Capability and Performance Ratios

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

Calculation 4. Cp calculation for characteristic H.

Cpk-Formula-Upper-Calculation-image

Calculation 5. Cpk upper calculation for characteristic H.

Cpk-Formula-Lower-Calculation-image

Calculation 6. Cpk lower calculation for characteristic H.

Group Short Run Xbar-R Chart Advantages

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

 

Group Short Run Xbar-R Chart Disadvantages

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

 

Additional Comments About the Case

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

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

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

Group Target Xbar-R Chart Example

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

How Do You Use Group Target Xbar-R Charts?

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

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

Case Description

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

Bring SPC Charts Up to Speed

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

Sampling Strategy

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

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

Data Collection Sheet

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

Group Target Xbar-R Chart

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

Chart Interpretation

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

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

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

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

 

Recommendations

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

Estimating the Process Average

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

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

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

Estimating Sigma

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

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

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

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

Calculating Process Capability and Performance Ratios

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

Calculation 4. Cp calculation for diameter a.

Cpk-upper-calculation-formula-img-2

Calculation 5. Cpk upper calculation for diameter a.

Cpk-lower-calculation-formula-img-3

Calculation 6. Cpk lower calculation for diameter a.

Group Target Xbar-R Chart Advantages

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

 

Group Target Xbar-R Chart Disadvantages

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

 

Additional Comments About the Case

  • The remaining process statistics and process capability and performance ratios for diameters b and c 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 a, b, and c. Although the dimensions of the poppet could also be monitored using three separate Xbar-R charts—one for each dimension—quality assurance wants to monitor the diameter using only one chart. This is why the group Xbar-R chart is selected.

Bring SPC Charts Up to Speed

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

 

LEARN MORE ABOUT MODERN SPC SOLUTIONS.

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

Data Collection Sheet

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

Group Xbar-R Chart

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

Chart Interpretation

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

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

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

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

 

Recommendations

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

Estimating the Process Average

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

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

Estimating Sigma

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

Calculation 2. Calculation of R for location a.

Calculation 3. Estimated standard deviation for location a.

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

 

Calculating Process Capability and Performance Ratios

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

Calculation 4. Cp calculation for location a.

Cpk-upper-calculation-sigma-img-2

Calculation 5. Cpk upper calculation for location a.

Cpk-lower-calculation-sigma-img-3

Calculation 6. Cpk lower calculation for location a.

Group Xbar-R Chart Advantages

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

 

Group Xbar-R Chart Disadvantages

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

 

Additional Comments About the Case

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

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

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

Short Run Xbar-R Chart Example

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

How Do You Use Short Run Xbar-R Charts?

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

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

Case Description

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

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

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

Bring SPC Charts Up to Speed

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

LEARN MORE ABOUT MODERN SPC SOLUTIONS.

Sampling Strategy

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

Data Collection Sheet

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

Short Run Xbar-R Chart

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

Chart Interpretation

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

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

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

Recommendations

30º Bend Angles

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

45º Bend Angles

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

90º Bend Angles

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

Estimating the Process Average

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

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

Estimating Sigma

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

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

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

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

 

Calculating Process Capability and Performance Ratios

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

Cpk-Formula-Upper-Calculation-img-2

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

Cpk-Formula-Lower-Calculation-img-3

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

Short Run Xbar-R Chart Advantages

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

 

Short Run Xbar-R Chart Disadvantages

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

 

Additional Comments About the Case

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

Cp-Cpk-calculations-img

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

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

Using the Target Xbar-R Chart: Example

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

How Do You Use Target Xbar-R Charts?

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

igure 1. Relief valve with adjustable cracking pressure capabilities.

Case Description

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

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

Bring SPC Charts Up to Speed

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

LEARN MORE ABOUT MODERN SPC SOLUTIONS

Sampling Strategy

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

Table 1. Crack pressure requirements for three valve customers.

Data Collection Sheet

Table 2. Data collection sheet for relief valves.

Target Xbar-R Chart

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

Control Limit Calculations

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

Calculation 2. Calculations for the crack pressure range chart.

Chart Interpretation

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

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

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

Recommendations

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

Assuming the targets are desired values,

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

 

Estimating the Process Average

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

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

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

 

Estimating Sigma

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

Calculation 4. Estimating sigma using R.

Calculating Process Capability and Performance Ratios

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

Calculation 5. Cp calculation for customer A valves.

Calculation 6. Cpk upper calculation for customer A valves.

Calculation 7. Cpk lower calculation for customer A valves.

Target Xbar-R Chart Advantages

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

 

Target Xbar-R Chart Disadvantages

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

 

Additional Comments About the Case

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

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

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

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Individual X and Moving Range (IX-MR) Chart

Learn how to use this two-chart combination view to keep key characteristics within control limits.

What is the Individual X and Moving Range Chart?

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

IX-MR Charts for a Single Characteristic

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

Scroll down to learn how to use this chart.

Automate and Simplify Control Chart Analysis

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

How to Use the IX-MR Chart

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

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

Advantages and Disadvantages of Using the IX-MR Chart

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

Advantages

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

Disadvantages

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

Decision Tree

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

Special Uses

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

Target IX-MR Chart

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

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

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

Short Run IX-MR Chart

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

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

Group IX-MR Chart

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

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

Group Target IX-MR Chart

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

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

Group Short Run IX-MR Chart

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

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

Group IX-MR Chart Example

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

How Do You Use Group IX-MR Charts?

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

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

Case Description

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

Bring SPC Charts Up to Speed

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

Sampling Strategy

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

Data Collection Sheet

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

Plot Point Calculations

The Group IX Chart

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

The Group MR Chart

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

Group IX-MR Chart Plot Points

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

Group IX-MR Chart

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

Chart Interpretation

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

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

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

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

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

Recommendations

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

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

Estimating the Process Average

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

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

Estimating Sigma

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

Estimating-Sigma-Value-image

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

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

Calculating Process Capability and Performance Ratios

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

Calculation 3. Cp for location a.

Cpk-upper-calculation-formula-2

Calculation 4. Cpk upper for location a.

Cpk-lower-calculation-formula-3

Calculation 5. Cpk lower for location a.

Group IX-MR Chart Advantages

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

Group IX-MR Chart Disadvantages

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

Additional Comments About the Case

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

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

Group Short Run IX-MR Chart Example

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

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

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

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

Case Description

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

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

Bring SPC Charts Up to Speed

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

Sampling Strategy

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

Target Values

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

Data Collection Sheet

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

Group Short Run IX-MR Chart

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

Chart Interpretation

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

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

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

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

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

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

Recommendations

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

Estimating the Process Average

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

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

Estimating Sigma

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

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

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

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

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

Calculating Process Capability and Performance Ratios

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

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

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

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

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

Group Short Run IX-MR Chart Advantages

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

Group Short Run IX-MR Chart Disadvantages

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

Additional Comments About the Case

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

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

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

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

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

Group Target IX-MR Chart Example

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

How Do You Use Group Target IX-MR Charts?

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

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

Case Description

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

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

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

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

Bring SPC Charts Up to Speed

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

Sampling Strategy

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

Data Collection Sheet

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

Plot Point Calculation

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

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

Group Target IX-MR Chart

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

Chart Interpretation

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

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

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

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

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

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

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

Recommendations

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

Estimating the Process Average

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

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

Estimating Sigma

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

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

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

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

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

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

Calculating Process Capability and Performance Ratios

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

Calculation 4. Cp calculation for seat key characteristic a.

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

Cpk-upper-calculation-image

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

Group Target IX-MR Chart Advantages

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

Group Target IX-MR Chart Disadvantages

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

Additional Comments About the Case

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

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

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

Short Run IX-MR Chart Example

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

Short Run IX-MR Charts

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

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

Case Description

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

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

Bring SPC Charts Up to Speed

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

Sampling Strategy

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

Data Collection Sheet

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

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

Short Run IX-MR Chart

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

Chart Interpretation

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

Recommendation

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

Estimating the Process Average

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

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

Estimating Sigma

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

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

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

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

Calculating Process Capability and Performance Ratios

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

Cpk-lower-calculation-image

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

Short Run IX-MR Chart Advantages

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

Short Run IX-MR Chart Disadvantages

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

Additional Comments About the Case

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

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

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

Target IX-MR Chart Example

Evaluate process control for part numbers with different target values.

How Do You Use Target IX-MR Charts?

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

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

Case Description

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

Bring SPC Charts Up to Speed

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

Sampling Strategy

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

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

Data Collection Sheet

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

Target IX-MR Chart

Figure 2. Percent solids target IX-MR chart.

Calculations for the MR Chart

Calculation 1. Calculations for MR chart.

MR Chart Interpretation and Recalculation

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

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

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

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

Calculations for the Target IX Chart

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

Target IX Chart Interpretation

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

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

Recommendation

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

Estimating the Process Average

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

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

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

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

Estimating Sigma

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

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

Estimating-Sigma-MR-Chart-2

Calculation 6. Estimating sigma using MR from Calculation 5.

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

Calculating Process Capability and Performance Ratios

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

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

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

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

Cpk-upper-calculation-3

Calculation 9. Cpk upper calculation for paint spec A.

Cpk-lower-calculation-4

Calculation 10. Cpk lower calculation for paint spec A.

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

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

Target IX-MR Chart Advantages

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

Target IX-MR Chart Disadvantages

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

Additional Comments About the Case

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

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

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

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

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Process Capability (Cp) and Performance (Cpk)

Learn how to determine whether your process is meeting its full potential—and see opportunities for improvement.

How do you use Cp and Cpk?

Although statistical process control (SPC) charts can reveal whether a process is stable, they do not indicate whether the process is capable of producing acceptable output—and whether the process is performing to potential capability.

Capability (Cp) and performance (Cpk) indices go beyond elemental quality control to illustrate a process’s ability to meet specifications. Using information from these statistics, you can better understand which processes need improvement, where you have opportunities for improved productivity, and how to prioritize improvement activities.

Let’s take a look at the difference between Cp and Cpk.

Multilevel Pareto Charts

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

What Is the Process Capability Ratio (Cp)?

Process capability analysis with the Cp ratio shows how well the process spread (expressed as six standard deviations) fits into the specification range. This measurement is determined by dividing the specification limit (voice of the customer) by the process spread (voice of the process).

To calculate Cp, subtract the lower specification limit from the upper specification limit, then divide by six standard deviations.

What Is the Process Performance Ratio (Cpk)?

The Cpk ratio shows the relationship of the process spread to the specification limits while taking into account the centering of the process compared to the specification limits. Cpk represents the lowest value of the capability against the upper or lower specification, showing where, within the specification limits, the process is producing.

To calculate Cpk, compare the average of the data to both the upper and lower specification limit. An off-centered process will have a greater risk of fallout to the specification limit closest to the process mean. The reported Cpk will be the one that measures the highest risk.

Cp-vs-Cpk-image

Evaluating the Relationship Between Cp and Cpk

Before relying on the Cp and Cpk values:

  • Verify that process variability is stable, i.e. no out-of-control patterns on the control charts.
  • Review individual data values on a histogram chart to verify that the distribution is normal (or close to normal).
  • Verify that engineering tolerances are known.
  • Verify that the estimated standard deviation of the process is known.

Never attempt to interpret numerical summaries of capability without also looking at a histogram of the data plotted against specification limits. Capability studies should also include analysis of control charts and capability indices.

Easily Determine Process Capability & Performance

When you use SPC software from InfinityQS, determining capability becomes easier than ever. See how to turn Cp and Cpk values into actionable information.

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Pareto Chart

Quickly identify the sources of your most frequent defects.

What is a Pareto Chart?

Pareto charts display defect codes and causes in a simple, easy-to-understand bar chart. But don’t let their simplicity fool you—these charts can be useful statistical process control (SPC) analysis controls.

A traditional use of a Pareto chart like the one shown here would be to count and categorize the types of potential defects that result from a visual inspection of an engine. You can see from this example that the defect “Incorrect Torque” is most prevalent.

Multilevel Pareto Charts

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

InfinityQS has turned the pedestrian Pareto chart into a robust, sophisticated analysis tool that allows sorting and display of defect codes any way you want—by shift, customer code, employee, lot number, part, time, and more. Any information associated with defect data can be sorted, sliced, and diced.

The two-level Pareto chart shown here includes the same defects as the previous chart but re-sorts the data by engine serial number (yellow bars), then by defect code (blue bars). Clearly the most prevalent defect is “Incorrect Torque,” but the re-sorting reveals additional information including:

  • The engine serial number where the most defects were found
  • The total number of defects for each engine
  • The type of defects found on each individual engine serial number
  • The fact that not all engines include “Incorrect Torque” defects

In our free webinar Box Plots and Pareto Charts, you’ll learn how to gain the greatest benefit from these tools. You’ll learn best practices, how to easily analyze data, and how to use weighting to monetize quality issues.

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Automate and Simplify Control Chart Analysis

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

See the Pareto Chart in Action

With the power of multilevel Pareto charts,InfinityQS solutions make it simple to identify and prioritize your most important quality improvement activities.

See how InfinityQS reveals valuable quality information and makes SPC easy.

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Statistical Process Control 101

Learn all about SPC for manufacturing.

The Problem with Tampering

When a process is centered on target and is in state of statistical control, any adjustments to the process only increase variation. Adjusting a process that is in control is referred to as tampering.

The Funnel Experiment and Deming’s Four Rules

The classic analysis of the effects of tampering is Deming’s Funnel Experiment. In this experiment, participants drop marbles through a funnel suspended over a target. The funnel represents the process, the marble drop location is the feature being produced, and the target is the customer specification.

Deming described four approaches—also referred to as rules—that encompass the typical ways in which the experiment participants tamper with the funnel (Out of Crisis, 1986, p. 328).

Rule 1: No adjustment

The optimal approach is to leave the funnel fixed and aimed at the target, without making any adjustments. When a process is stable, centered, and shows only the inherent variation, there is no reason to make an adjustment.

The takeaway: Before attempting any process adjustment, you must gather enough data to make sure you understand the normal behavior of the process. Use a control chart to track variations, and then adjust the process only when special variations occur.

 

Rule 2: Adjustment from last position

Sometimes referred to as the “human nature” approach, some participants move the funnel after each drop, to try and compensate for the previous drop’s variation. In this approach, the funnel is moved the exact negative distance of the drop. Compensating for the “error” of the drop, might improve the on-target average but doubles the variation.

The takeaway: When participants compensate for error, the variation doubles—and remember, variation is the true issue. This problem is prevalent in gauge calibration when manufacturers adjust a gauge after taking one standard measurement.

 

Rule 3: Adjustment from target

Participants trying to take a “logical” approach also move the funnel to try to compensate for the previous drop. But in this instance, the funnel is moved not based on its last location, but on its distance from the target. For example, if the measurement of the previous drop was 5 units above the target, participants move the funnel 5 units below the target.

The takeaway: Although this approach seems logical, it results in an oscillating process.

 

Rule 4: Adjustment from last drop

In this approach, participants move the funnel to point at the previous drop rather than the target. In other words, at drop n, they set the funnel over the location of the n-1 drop. As you might expect, this approach creates a pattern that moves steadily away from the target.

The takeaway: Believe it or not, this approach occurs in calibration scenarios when one product is used to set up for the next production. This issue is typical in workplaces where on-the-job training is prevalent.

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Statistical Process Control 101

Learn all about SPC for manufacturing.

Statistical Process Control (SPC) Implementation

Statistical process control is certainly not the only technique used to improve processes. But for our purposes here, we will focus on two of the tools used most in SPC:

  • Histograms
  • Control charts

LEARN MORE: SPC TOOLS FOR ANALYSIS

Histogram

Histograms can provide a quick view of process variation and are used to plot frequency distributions.

Control chart

Control charts are the best-known tools associated with SPC.

Control charts are used to determine whether a process is stable or unstable. There are many types of control charts that can be used to fit the nature of different types of data streams and sampling methods.

Below are examples of the most commonly used control charts:

  • Variable data
    • Xbar-S: Xbar and standard deviation
    • Xbar–R: Xbar and range chart
    • IX–MR: Individual X and moving range chart
  • Attribute data
    • c: Defect count
    • u: Defect count, normalized to sample size
    • p: Proportion defective
    • np: Proportion defective multiplied by sample size

Control charts are discussed further in the Process Behavior and SPC Control Charts section as well as in our Definitive Guide to SPC Charts.

LEARN MORE: DEFINITIVE GUIDE TO SPC CHARTS

Although SPC charts are revealing, today’s manufacturers increasingly recognize the benefits of moving away from manual SPC—conducted by recording data on paper and then running analysis via offline spreadsheets or statistical software—and instead using real-time SPC software.

SPC Software

Quality control software for manufacturing offers multiple benefits:

  • Surface relevant information more quickly
  • Filter data according to role (e.g., operator, quality manager) and location (e.g., the lines being worked on that day)
  • Faster, focused, and more detailed analysis
  • Additional means of evaluating data (e.g., grading and stream summary)
  • Directed alerts and notifications
  • Mobile, enterprise-wide visibility into operations

InfinityQS is the leading provider of SPC software and services for manufacturers, providing quality intelligence solutions that work in the cloud or on-premises, across the globe.

LEARN MORE: SPC SOFTWARE FOR MANUFACTURING

Remember: Using statistical process control just to “put out fires”—finding an out-of-control point on a control chart and then determining and removing the assignable cause—is not the same as creating continuous improvement. SPC can be fully realized only when you use it to improve processes and reduce variation.

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Statistical Process Control 101

Learn all about SPC for manufacturing.

Statistical Process Control FAQs

Still have questions about statistical process control (SPC)? Click the links below to locate information about popular topics.

What is SPC (statistical process control)?

Statistical Process Control (SPC) is a scientific, data-driven methodology for quality analysis and improvement. In manufacturing, SPC is an industry-standard methodology for measuring and controlling quality during the manufacturing process.

LEARN MORE:  WHAT IS SPC?

What are the origins of SPC?

Dr. Walter A. Shewhart (1891–1967), a specialist in the use of statistical methods, was responsible for the application of statistical methods to process control. Up until Shewhart, quality control methods were focused on inspecting finished goods and sorting out the nonconforming product. As an alternative to inspection, Shewhart introduced the concept of continuous inspection during production and plotting the results on a time-ordered graph that we now know as a control chart.

LEARN MORE: SPC 101

How does SPC relate to quality control in manufacturing?

By using statistical process control, manufacturers can move from a detection approach to a prevention approach, reducing or eliminating the need to rely on sorting or inspection. SPC can increase productivity, reduce waste, and reduce the risk of shipping nonconforming products.

LEARN MORE: WHY USE SPC IN MANUFACTURING?

How can I implement an SPC measurement system?

Control charts are used to determine whether a process is stable or unstable. However, using statistical process control just to “put out fires”—finding an out-of-control point on a control chart and then determining and removing the assignable cause—is not the same as creating continuous improvement. SPC can be fully realized only when you use it to improve processes and reduce variation.

LEARN MORE: STATISTICAL PROCESS CONTROL IMPLEMENTATION

What are statistical process control limits?

Control limits are calculated from the process itself. Because control limits show how the process is performing, they are also referred to as the “voice of the process.” Control limits show how the process is expected to perform; they show the variation within the system or the range of the product that the process creates.

LEARN MORE: SPECIFICATION AND CONTROL LIMITS

What are specification limits?

Specification limits are boundaries set by a customer, engineering, or management to designate where the product must perform. Specification limits are also referred to as the “voice of the customer” because they represent the results that the customer requires. If a product is out of specification, it is nonconforming and unacceptable to the customer.

LEARN MORE: SPECIFICATION AND CONTROL LIMITS

What are Shewhart statistical process control charts?

All control charts have three common elements:

  • Plot points: Plot points usually represent individual measurements, averages, standard deviations, or ranges.
  • Centerline: The centerline is usually (but not always) the average of the points plotted on the chart.
  • Control limits: Control limits represent the amount of variability in the process.

There are four foundational guidelines to Shewhart statistical process control charts.

LEARN MORE: SPC CONTROL CHARTS

What’s the best use of SPC control charts?

Control charts are used to determine whether a process is stable or unstable. There are many types of control charts that can be used to fit the nature of different types of data streams and sampling methods.

LEARN MORE: STATISTICAL PROCESS CONTROL (SPC) IMPLEMENTATION

How should I use SPC charts to determine process capability?

Capability is calculated from existing data but can be used as a prediction of future performance. However, the capability results must come from an in-control process if the results are to be used to predict the process’s behavior in the future. The most commonly used measures of capability are Cp, Cpk, Pp, and Ppk.

LEARN MORE: PROCESS CAPABILITY

Why do SPC initiatives fail, and how can I help ours succeed?

Statistical process control can help manufacturers achieve continuous process improvement—when it is implemented properly. Watch out for obstacles that can sideline your SPC efforts.

LEARN MORE: OVERCOMING OBSTACLES TO EFFECTIVE SPC

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