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In modern manufacturing organizations, quality professionals seek to tightly manage every step in every process to ensure consistent quality—a task that becomes more challenging as production lines cross staff, processes, and plants.
Using statistical process control (SPC) for quality improvement can alleviate some of the complexity. SPC brings a systematic approach to data collection and analyses, no matter where they occur. Quality team leaders set the expectations for data collection (i.e., what, when, and how), and establish acceptable deviations. Unfortunately, traditional quality control in manufacturing ends there. The value of that data is often limited to a single use, verification of compliance, or an adjustment justification.
A central data repository extends the benefits of SPC by making the quality data you collect accessible throughout the organization, whether that’s on the plant floor or in the executive board room. With a single repository for quality data, commonly “siloed” information comes together to create a singular, company-wide picture of quality.
Making quality data consistent, accessible, and actionable empowers every team member to put quality first.
Standardization and centralization of data establishes a common language—and expectation—surrounding quality that cascades throughout the organization. When every team member is using the same playbook, some of the complexity dissipates. In its place, manufacturing organizations can introduce ways to improve quality and productivity.
Quality-focused teams can realize greater benefits from their statistical process control efforts.
Manual data collection can lead to “garbage in, garbage out,” wasting the time and resources it takes to collect and analyze the data. Handwritten data can be difficult to interpret, and paper reports can become lost or damaged. If data is missing or indecipherable during an audit, the results can be costly.
InfinityQS solutions enable semi-automated and automated data collection, as well as automated alerts and notifications, to ensure checks are completed and data is accurate. And centralizing your data in a single repository helps you build a clear picture of quality across the organization.
Siloed data leads to slower decision-making. In contrast, InfinityQS quality improvement solutions make it easy for you to access data in real time—by production line, plant, or region—at the same pace you need to make quality decisions. Operations managers and quality team members know the moment an issue arises so they can take steps to preserve quality or avoid costly missteps.
With a centralized data repository, empowered users can create and pull reports when they need them, without waiting for IT to merge data from multiple systems or manage a massive export. With accurate and complete data, you can easily plot a continuous improvement journey.
With accessible, data-backed insights, quality teams can find the most influential quality initiatives to undertake as a company—by region, product, or plant. InfinityQS solutions help you spot transformative opportunities that might otherwise be buried in spreadsheets or stuck in an operational silo. And purpose-built analytical tools help you determine which initiatives will deliver the biggest and fastest ROI.
Quality control in manufacturing is intended to save time and money—not drain resources or become just one more cost center. Quality management software solutions from InfinityQS help your whole quality team increase profits by improving some of the costliest manufacturing metrics like scrap and rework, unplanned downtime, overtime, defect costs, and warranty claims.
Ready to empower every team member to put quality first? Take a peek at the features, analytics, dashboards, and reports in InfinityQS software to see how you can improve quality using data you already have.
Putting actionable information into the hands of every empowered team member—from operators to quality professionals to executive leaders—prevents quality disruptions and moves the organization toward quality manufacturing best practices. Working together, you can achieve stronger quality outcomes that transform the entire enterprise, such as:
InfinityQS quality improvement solutions bring data and people together throughout the manufacturing process. The result is greater efficiency, better product consistency, and overall higher manufacturing quality.
What to Expect
Modern manufacturers have two choices: to simply meet quality and regulatory standards or to pursue manufacturing excellence and reset the bar. Which do you choose?The insight you need to break through quality barriers and transform your manufacturing organization is within reach. It’s in your quality metrics. The metrics you measure are more than just report cards and to-do lists. They can help you adapt, thrive, and thrill customers with reliably high quality. The challenge is being able to see into that vast amount of data to determine which quality initiatives should rise to the top.The key is to standardize and centralize your quality data in a single repository. Once performance data from different quality systems are unified, they can be turned into manufacturing intelligence.
Stop solving problems and start pursuing excellence. Use quality metrics to launch a perpetual cycle of continuous improvement.
What would happen if you only read 2% of your emails? You’d miss a lot.
That’s exactly what many manufacturing organizations are doing with their collected data; they dig deep into exception data and ignore the majority of their quality metrics. By doing so, they miss opportunities to make substantive, system-wide improvements.
InfinityQS quality improvement software aggregates a variety of quality metrics—and yes, this includes in-spec data, so it’s easy to compare performance across lines, parts, plants, and other key factors. Whether data are collected manually or through automation, they all flow into one place. Then the data are standardized so access to the information and analysis becomes easy, and you can see the “big picture” of quality across the organization.
Statistical process control (SPC)-driven dashboards and control charts bring quality priorities into focus. With access to this clarified data in real time, your busy executives can identify opportunities for huge improvements in quality, customer satisfaction, and profitability.
InfinityQS solutions help leaders model process capability so they can evaluate the impacts of quality improvement initiatives—and prioritize those that will have the most value.
Data stream grading, for example, enables executives to visually expose and isolate those areas of potential improvements. All streams of data are given a score based on actual performance versus expected performance, giving leaders a clear picture of what’s working, where they need to deploy Six Sigma support, and what they stand to gain.
Simple color-coded matrices show leaders where to capture “quick wins” and which processes will deliver transformational improvement.
With detailed metrics at their fingertips, executives gain visibility across the entire enterprise. Quality excellence that’s achieved in one plant or line can be replicated across the organization to maximize the impact and multiply return on investment (ROI). Even with limited resources, quality manufacturing leaders can turn data into intelligence and better-informed decisions.
All of your quality metrics matter—not just the defects or “lessons learned.” InfinityQS quality improvement solutions collect and combine all of your quality data into a single system so you can compare and improve performance across the enterprise. See what’s happening in your organization in real time and over time.
InfinityQS helps manufacturers prevent quality issues rather than simply respond to them. Built to support quality manufacturing with real-time SPC, InfinityQS software gives leaders the information they need to predict quality outcomes, when and where they need it.
Dashboards transform key quality data into digestible summaries, so quality leaders can take proactive steps to reduce risk, increase efficiency, improve profitability, and produce top-quality products.
In modern manufacturing, it’s not enough to know what happened yesterday. To achieve quality excellence, you need to know what’s happening right now, what will happen if you take action, and where to begin.
Statistical process control (SPC) standardizes the processes that manufacturers use to collect and analyze quality data. Using SPC, manufacturers become better at predicting outcomes and improving their quality manufacturing processes.
When teams are working to improve quality in real time, they reduce the lag between data collection and proactive corrective actions.
InfinityQS solutions enable real-time data to flow seamlessly into existing workflows right “out of the box.” Once quality data are entered, they are saved to the unified data repository, building a comprehensive view of quality that can be dissected and analyzed across any number of factors, from product code to production line or geographic site.
The information is accessible and actionable too. Using easy-to-read dashboards and alerts, empowered team members can see where they need to focus their attention—right now—to protect quality and eliminate waste.
Time is money. InfinityQS solutions ensure that critical quality data is collected, analyzed, and put to use immediately.
Enable teams to take action and improve quality in real time.
To protect your company’s reputation and earning potential, you need to predict and prevent quality issues before they become full-scale problems. Once products fail in the field, are recalled, or generate customer complaints, recovery can be difficult (and costly) for manufacturers.
InfinityQS quality improvement solutions create a centralized and standardized place for your quality manufacturing data to reside. Real-time data collection, dashboard-level reporting, and automated alerts empower quality teams to act on the data in real time to head off quality problems.
Intervening early saves manufacturers from costly rework, scrap, waste, and upset customers. InfinityQS software gives operators, quality teams, and executives the information they need to control quality and maintain continuous improvement.
To maintain top quality manufacturing, operators and quality teams need data in real time. InfinityQS enables data collection, analysis, and reporting in real time so you can take steps to consistently protect quality. Right now.
The ability to monitor and analyze real-time data from anywhere can save manufacturers millions of dollars. With real-time data, manufacturers can reduce waste and scrap, prevent defects and recalls, and empower operators to protect quality.
Machines or processes that are producing out-of-spec products or parts can waste time and materials, and even lead to product recalls. InfinityQS quality improvement solutions help manufacturers identify issues and pinpoint problem areas in real time and along the entire manufacturing process—not just during final testing.
InfinityQS helps manufacturers continually measure and improve their operations by:
InfinityQS solutions enable users to monitor and respond to real-time quality data from any location, any time. Your data are stored in a centralized repository and standardized to accommodate detailed investigations into defect codes, shifts, customer codes, employees, lot numbers, or parts.
InfinityQS solutions give operators, engineers, and plant managers the tools and insight they need to identify, prioritize, and drive quality improvement.
At the corporate level, one person may oversee several products, plants, or regions. A unified data repository that’s updated and accessible in real time helps off-site managers stay tightly connected to daily operations—even at remote facilities.
When quality leaders have accurate and timely information at their fingertips, manufacturing organizations gain the following benefits:
A leading North American consumer packaged Food and Beverage company needed to decrease plant-to-plant manufacturing variations and reduce waste. The company leveraged InfinityQS SPC-driven and cloud-based quality management software to pool real-time manufacturing data from six sites and a corporate lab into a single, secure data repository.
With immediate access to real-time performance data, the quality assurance team was able to quickly find and respond to fluctuations in data. See what they uncovered—and how it changed the business.
Read the case study
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.
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:
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.
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.
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.
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.
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.
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.
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.
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:
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 supports all the most commonly used SPC tools, such as:
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.
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:
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.
Learn how to use this combined view to track variation across across a single characteristic—and pinpoint issues at a glance.
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.
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.
See how easy it is to access actionable information from your SPC control charts.
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.
Use the following decision tree to determine whether the Xbar-R chart is the best choice. Scroll down to see special use examples.
Today, control charts are a key tool for quality control and figure prominently in Lean manufacturing and Six Sigma efforts.
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.
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.
Group Xbar-R charts help you assess changes in averages and the range of averages across measurement subgroups for a characteristic.
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.
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.
Simplify process monitoring by representing data for multiple parts and multiple characteristics on one chart.
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.
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.
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.
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).
Table 2. Data collection sheet for the group short run Xbar-R chart lathe example. MAX and MIN plot points are shown in bold.
Figure 2. Group short run Xbar-R charts representing two parts and multiple characteristics.
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.
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.
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.
Calculations 4, 5, and 6 show the process capability and performance calculations for characteristic H.
Calculation 4. Cp calculation for characteristic H.
Calculation 5. Cpk upper calculation for characteristic H.
Calculation 6. Cpk lower calculation for characteristic H.
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.
Get visibility into process and part variability at a granular level.
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.
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.
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.
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.
Table 1. Group target Xbar-R chart data for three sleeve characteristics. MAX and MIN plot points are shown in bold.
Figure 2. Group target Xbar-R chart representing three different sized inside-sleeve diameters.
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.
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.
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.
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.
Calculations 4, 5, and 6 show the process capability and performance calculations for diameter a.
Calculation 4. Cp calculation for diameter a.
Calculation 5. Cpk upper calculation for diameter a.
Calculation 6. Cpk lower calculation for diameter a.
Table 2. Additional statistics and process capability and performance values for diameters b and c.
Check uniformity of multiple key characteristics on a single chart.
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.
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.
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.
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.
Table 1. Data collection sheet for the group Xbar-R chart. MAX and MIN plot points for each group are displayed in bold.
Figure 2. Group Xbar-R charts representing three ODs on the same part.
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.
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.
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.
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.
Calculations 4, 5, and 6 show the process capability and performance calculations for location a.
Calculation 4. Cp calculation for location a.
Calculation 5. Cpk upper calculation for location a.
Calculation 6. Cpk lower calculation for location a.
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.
Evaluate process control for short production runs and different part numbers.
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.
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.
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.
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.
Table 2. Spring-back data including short run plot point calculations.
Figure 2. Spring-back short run Xbar-R control charts.
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.
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.
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.
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.
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.
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.
Calculation 4. Cp calculation for the 30° bend angle spring-back.
Calculation 5. Cpk upper calculation for the 30° bend angle spring-back.
Calculation 6. Cpk lower calculation for the 30° bend angle spring-back.
The process capability and performance ratio calculations for the 45° and 90° bend angle spring-back are shown in Table 17.7.
Table 3. Cp and Cpk calculations for 45° and 90° bend angle spring-back characteristics.
See how a quality professional uses the target Xbar-R chart to ensure consistent process performance and meet specifications for different customers.
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.
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.
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
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.
Table 2. Data collection sheet for relief valves.
Figure 2. Crack pressure target Xbar-R control chart.
Calculation 1. Calculations for the crack pressure target Xbar chart.
Calculation 2. Calculations for the crack pressure range chart.
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.
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,
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.
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.
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.
Table 3. Cp and Cpk calculations for valves B and C.
Learn how to use this two-chart combination view to keep key characteristics within control limits.
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.
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.
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.
Use the following decision tree to determine whether the IX-MR chart is the best choice. Scroll down to see special use examples.
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.
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.
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.
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.
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.
Pinpoint product and process characteristics that are most in need of attention to ensure consistency.
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.
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.
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.
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.
Table 1. Group IX-MR chart data collection sheet. MAX and MIN plot points are shown in bold.
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 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.
Table 2. Group IX-MR chart plot point summary.
Figure 2. Group IX-MR chart for arc widths.
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.
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.
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.
Process average estimates should be performed separately for each characteristic or location on the group chart.
Estimates of sigma are also calculated separately for each characteristic or location on the group chart. Continuing with location a, see Calculation 2.
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.
Calculations 3 through 5 show the process capability and performance calculations for location a.
Calculation 3. Cp for location a.
Calculation 4. Cpk upper for location a.
Calculation 5. Cpk lower for location a.
Table 3. Process capability and performance calculations for locations b and c.
Graphically illustrate variation in processes, products, and characteristics on one chart.
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.
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.
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.
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.
Table 2. Target values for compounds A, B, and C.
Table 3. Group short run IX-MR chart data collection sheet. MAX and MIN plot points are shown in bold.
Figure 2. Group short run IX-MR chart for three different compounded adhesive solutions.
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.
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.
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.
Calculation 4. Cp for percent solids content from compound C.
Calculation 5. Cpk upper for percent solids content from compound C.
Calculation 6. Cpk lower for percent solids content from compound C.
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.
Table 4. Process capability and performance calculations for compound C’s chemical 1, clarity, and reactant temperature.
Spot sources of variation unique to a process, product, and characteristic—on a single chart.
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.
Three generic key characteristics are monitored on several different seat products. All seats share three common key characteristics and tolerances.
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.
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.
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.
Table 2. Group target IX-MR data and plot points (shown in bold) for the three seat product line characteristics.
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.
Figure 2. Group target IX-MR chart used to evaluate three different key characteristics from three similar parts.
Group MR chart: MAX and MIN plot points from consecutive groups appear to be descending over time. This could be the result of either
With more data, this initial observation could be confirmed or rejected.
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.
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.
Estimates of sigma are also calculated separately for each characteristic on the group chart. Continuing with key characteristic a, see Calculations 2 and 3.
Calculation 2. Calculation of MR for key characteristic a across all seat series.
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.
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.
Calculation 6. Cpk lower calculation for seat key characteristic a.
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.
Assess process control for short production runs between different part numbers.
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.
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.
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.
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.
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.
Figure 2. Bottle burst test data short run IX-MR control chart.
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.
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.
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.
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.
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.
Calculation 4. Cpk lower calculation for bottle type A burst pressure.
Table 3. Additional summary statistics and process capability and performance ratios for remaining bottle types.
Evaluate process control for part numbers with different target values.
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.
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.
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.
A target IX-MR chart is used to monitor this process because
Table 1. Data collection sheet for constructing target IX-MR chart.
Figure 2. Percent solids target IX-MR chart.
Calculation 1. Calculations for MR chart.
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.
Calculation 3. Calculations for the percent solids target IX chart.
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.
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.
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.
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.
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.
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.
Calculation 9. Cpk upper calculation for paint spec A.
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.
Cp and Cpk for paint specifications D and E are shown in Table 2.
Table 2. Cp and Cpk values for paint specifications D and E.
Learn how to determine whether your process is meeting its full potential—and see opportunities for improvement.
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.
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.
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.
Before relying on the Cp and Cpk values:
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.
When you use SPC software from InfinityQS, determining capability becomes easier than ever. See how to turn Cp and Cpk values into actionable information.
Quickly identify the sources of your most frequent defects.
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.
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:
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.
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.