Complexity in operations can drive up manufacturing costs and frustrate manufacturing teams.
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Complexity lurks in many corners of the manufacturing plant:
Using modern statistical process control for quality improvement helps to combat complexity by providing a means to understand and strategize around expected, standard variations in process quality.
Many SPC quality systems promise to help improve processes—but then require extensive effort or additional expenses to integrate with existing infrastructure. Not so with Enact®, a cloud-based quality solution that is easy to try, use, and buy. Enact doesn’t require changes to your existing infrastructure, or the purchase of additional “modules” to achieve full functionality.
Enact can help your operations and quality improvement teams ramp up and start using SPC quickly, with intuitive UIs and extensive self-help. Not only does this reduce stress and slow-downs on the line, but your IT resources are also freed up for other tasks.
Enact uses process models and part recipes to provide a clear visualization of your manufacturing processes. With SPC that works like you do, you simplify the data collection process and reduce the burden on operators. Plus, this type of visual mode creates a reference that enables input from multiple sources and helps to clarify and streamline communication.
With Enact, you don’t need to jump through multiple hoops to see the “big picture” of manufacturing quality data. Customizable dashboards help cut down on complexity by showing you what you need, when you need it.
Audits can cost manufacturers thousands in lost time—and those are the ones that go right.
For manufacturers, industry audits are typically a stressful endeavor. Depending on your industry, regulations and compliance issues can be complicated, overwhelming—and devastating, if not followed and documented correctly. With an audit on the horizon, it can be difficult to find the time to locate, compile, and present the requested data while staying on top of all your regular day-to-day tasks. A statistical process control (SPC) system can help ease the process, giving you a more efficient way to collect, store, and retrieve quality and operations data.
With Enact®, you can easily prove that checks were completed correctly and on time. You can create reports in minutes, pulling together quality, preventative control, and other data across one shift or multiple shifts on multiple days.
Easily create customized reports in response to specific auditor or customer queries (e.g., an exceptions report that shows only applicable alarms, events, assignable causes, and corrective actions).
Save expensive physical storage space with Enact’s secure, cloud-based environment—without sacrificing anywhere, anytime access.
Improve traceability with Enact, for more precise tracking in the event of a problem with the quality of raw materials or finished product. Improved responsiveness in such situations can help to mitigate damage to your brand.
Inefficiency is the enemy of manufacturing profit.
“Time is money,” the saying goes—and nowhere is it truer than in manufacturing. Ideally, you can produce as much quality product as possible in the span of any given hour—without inefficient processes siphoning off the resulting profits. Many manufacturers see quality-improvement efforts as a cost center, when in fact they can help to increase profits by improving efficiency across the board and helping to—
Enact® saves operator time by improving the efficiency of the data collection process, including the ability to pull in data from equipment that supports automated collection. Even for machines that require manual recording of data, entering that data directly into Enact is fast and easy. Plus, Enact supports the configuration of entry limits, so that any accidental typos or transpositions are easier to catch immediately.
Forget the hours and hours that many SPC systems demand when it comes to retrieving and analyzing quality data. With Enact’s Unified Data Repository, retrieving information, tracking trends, and responding to reporting, customer, or audit demands takes a fraction of the time other systems require.
Unlike other SPC systems, Enact makes it possible to compare multiple products, shifts, processes—even sites—in a single chart. No need to export data for further calculations in Excel or Minitab; with Enact, you have robust, powerful analytic capabilities all from within your SPC system.
Thanks to Enact’s support for historical and aggregated analysis, you can more easily discover the approaches that lead to optimal quality. This ability supports the development of best practices, which can improve efficiency across your organization. And with Enact, you have the means to verify that such practices are being followed to the letter, across lines, shifts, and sites.
Non-conforming product can ruin your day, your reputation—and your manufacturing business.
The right statistical process control (SPC) solution can help you reduce or even eliminate the amount of defective product that comes off the production line—and thus the number of expensive recalls you must carry out. Recalls are costly in a multitude of ways:
Many manufacturers track multiple types of defects, including visual defects. Collecting this data at various intervals for multiple products can become time-consuming. With Enact®, you can collect such data in just one data entry configuration, yet configure separate system alarms for each defect type.
Enact supports the collection, notification, and analysis of both defectives (i.e., pass/fail on items) and defects (i.e., condition count). Multi-level Pareto charts enable the display of defect codes, sorted and displayed by shift, customer code, employee, lot number, part, or any tagged descriptor.
Further reduce defects by maintaining better traceability of raw materials. With Enact’s cloud-based, global, mobile capabilities, you can communicate and observe alerts and monitor quality from any location, 24/7.
Enact provides the precise, configurable data to support a Six Sigma implementation, helping your manufacturing organization extract optimal value from your quality data and reduce or eliminate defective products.
Out-of-spec product can rack up losses. SPC enables waste management in manufacturing.
A robust statistical process control (SPC) solution can reduce waste by helping your operations team spot critical out-of-spec dimensions. The earlier you catch such issues, the less wasted materials or recalled products you’ll need to deal with. InfinityQS SPC solutions provide the tools you need to catch process problems—fast. Together, we’ve helped our customers save millions of dollars in reduced waste.
You can’t stop waste if you can’t find it. Too many companies use guesswork to figure out why product isn’t up to snuff. But with Enact®, you can pinpoint how to reduce waste in manufacturing and significantly reduce costs throughout your operations.
When you test quality only at the finished product or final production stage, you can find yourself with staggering amounts of waste and scrap, in ruined product or rework time. Enact enables automatic notifications and staggered quality checks. That way, operators and quality personnel know immediately if a process, machine, or product falls out of spec—and can resolve the problem before it causes too much damage.
Enact enables a “big picture” view of whether processes are running smoothly or need attention. When you see trouble, it’s easy to drill down into the details of real-time SPC alerts and operations status, for better problem-solving and a faster resolution.
Fighting waste is a never-ending battle. With the power to roll up aggregated and historical data across processes, products, lines, and even sites, Enact gives you the ability to track trends and variations that lead to waste—even for processes and products that are within spec. As a result, InfinityQS customers have saved many millions of dollars.
Discover substantial benefits for your manufacturing organization when you modernize shop floor operations with new quality control tools and techniques.
Manufacturing has changed. Yet many manufacturers still approach quality improvement and statistical process control (SPC) with yesterday’s mindset and SPC tools. Why not meet these challenges with solutions that work with today’s technology and data loads, rather than keeping you stuck in the past?
InfinityQS® software—ProFicient™ for on-premises or Enact® in the cloud—brings SPC tools up to speed. With features that help you optimize and modernize data collection, analysis, and reporting, our solutions enable you to overcome today’s most pressing problems and challenges.
With InfinityQS Enact, Frost & Sullivan’s Best Practices Award winner for Product Leadership, implementing SPC software has never been easier—or more affordable. From low cost of entry to robust help systems, Enact is designed to make statistical process control tools work for you. Plus, our team of Six Sigma green and black belts understand quality and are ready to provide the tools and training you need to become a model of modern manufacturing success.
Can you afford not to improve your process quality? Not only does InfinityQS Enact break through traditional SPC price barriers, it enables additional profit potential simply by helping you update the way you deal with data.
Data Collection Save operations resources with more effective and efficient data collection.
Data Analysis Improve data analysis with extensive charting and comparison capabilities.
Data Reporting Respond more quickly to information demands with easier, faster reporting and data access.
Enact empowers you to quickly realize the benefits of digital data collection and analysis. Start today with:
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Prioritize quality and process control to reduce regulatory compliance risks, customer complaints, and recalls.
InfinityQS® solutions use proven statistical process control (SPC) methodology to help you prevent problems—and the associated risks.
Boost ROI From giving you the insight you need to monitor supplier quality to improving traceability and streamlining audits, InfinityQS solutions provide unbeatable ROI.
Protect brand equity Consistency is a hallmark of brand equity. How can you ensure that customers get the same high-quality product from any manufacturing site, at any time? How can you detect potential quality problems as quickly as possible—or better yet, spot the warning signs and prevent the problems? InfinityQS solutions provide targeted yet extensive data collection and capabilities, automated alerts, and aggregated access to historical data so that you can produce a consistently excellent product that meets brand expectations.
Reduce customer complaints Your customers demand high quality, reliable products. You need proven, efficient quality control methods to meet those demands. One faulty process can set back both production and customer loyalty. With InfinityQS, you get solutions that help you respond to customer needs—quickly, flexibly, and consistently.
Minimize recalls Product recalls are costly, not just in lost time and wasted materials but also in the potential loss of customer confidence and brand reputation. InfinityQS gives you the insight you need to reduce defect levels, automate policy and procedure enforcement, and reduce scrap and rework—all of which can help to prevent the dreaded recall.
Hundreds of InfinityQS clients responded to a survey we conducted, documenting savings in key metrics including scrap, rework, defects, cycle time, overtime, warranty claims, MRB/sorting, holds, escapes, data collection, reporting and recalls.
The average results are as follows:
Simplify compliance, streamline audits, and meet or exceed industry quality control standards, thanks to InfinityQS built-in features.
Whether you need to comply with government regulations, meet customer specifications, or simply aim to exceed industry quality control standards, InfinityQS® solutions include built-in features to make your work easier.
Meet Lean and Six Sigma requirements Process improvement methodologies like Six Sigma and Lean Manufacturing rely on solid data-collection plans and operational insight. InfinityQS gives you the ability to collect, aggregate, and analyze process and quality data to meet the demands of such programs.
Improve traceability and reduce recall risk The ability to find any part or focus in on any process is a must for reliable traceability—and in turn, can help to prevent or reduce recalls. But how can you expect agile, flexible responses to data queries when half the work of gathering or locating data is still being done on clipboards and in spreadsheets? InfinityQS solves this problem with automated, responsive capabilities that simplify collecting, aggregating, and analyzing data, enabling you to find the information you need, easily and swiftly.
Simplify audits InfinityQS quality and process optimization solutions provide automated, customizable, enterprise-wide quality- and process-data collection, analysis, and reporting so you can keep production moving and satisfy compliance and auditing demands. Keep throughput high and information at your fingertips.
Comply with regulations In today’s global market, you must juggle the details of multiple national and international regulations and compliance requirements. Meeting those expectations—and managing the reporting and downtime associated with audits and recalls—can drain time, energy, and resources. With InfinityQS, get automated notification when compliance checks are—or aren’t—performed and visibility into potential or actual failures.
Ensure specification compliance InfinityQS is ISO Certified 9001/2001, so you can have confidence in both quality and security controls.
In high-speed operations with large sample sizes and automated data collections, use this chart to maintain consistency of key characteristics.
The Xbar chart (the upper chart in this figure) plots the average of individual values in a subgroup (i.e., the subgroup mean). The s chart (the lower chart in the figure) plots the sample standard deviation of the individual values in the subgroup. This combined chart is sometimes referred to as Xbar-SD.
For example, this sample chart (taken from InfinityQS® ProFicient™ software) highlights subgroup 9 of 20 subgroups. You can see that the average of the subgroup’s plot points is 34.02 (top chart) and the standard deviation is 2.755 (lower chart).
Scroll down to learn how to use this chart.
See how easy it is to access actionable information from your SPC control charts.
Use the Xbar-s chart chart when your sample size is 10 or more (n≥10). This scenario is most common when a lot of data is available (or necessary) and the data acquisition cost is low.
For example, you might use this chart for data taken from Programmable Logic Controllers (PLCs) or other automated data-collection devices. Injection molding, multihead fill operations, and continuous high-speed production lines on which many measurements can be gathered quickly and affordably are all good environments for this type of chart.
Each of the special use case examples described on this page presume a large sample size (i.e., 10 or more).
Use the following decision tree to determine whether the Xbar-s 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.
Short run charts are used for short production runs. The short run Xbar-s chart can help you identify changes in the averages and standard deviation of multiple characteristics, even those with different nominals, units of measure, or standard deviations.
Group charts display several parameters, characteristics, or process streams on one chart. Group Xbar-s charts help you assess changes in averages and the standard deviation across measurement subgroups for a characteristic.
The group target Xbar-s chart provides information about changes in process averages and the standard deviation across multiple measurement subgroups of similar characteristics that have a common process. Part numbers and engineering nominal values can differ across these characteristics.
The group short run Xbar-s chart enables you to spot changes in the process average and standard deviation across multiple characteristics in a short run environment.
Group short run Xbar-s charts enable you to spot changes in the process average and standard deviation across multiple characteristics in a limited production run. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group short run Xbar-s chart works.
Figure 1. Mechanical pencil with three key characteristics.
A company manufactures mechanical pencil lead. There are three key characteristics (see Table 30.5).
Table 1. Upper and lower specification limits for three mechanical pencil lead key characteristics.
The manager wishes to monitor the stability of all three key characteristics on the same chart.
Because production volume is very high and three different characteristics are to be monitored, a group short run Xbar-s chart is selected. Ten leads are tested every 30 minutes.
Preliminary tests on all three key characteristics were conducted. The purpose of the tests was to establish target values for the group short run charts to be used. The target values are found in Table 2.
Table 2. Target X and target s values for the three mechanical pencil lead key characteristics.
Table 3. Data collection sheet for the group short run Xbar-s chart pencil lead example. MAX and MIN plot points are shown in bold.
Figure 2. Group short run Xbar-s chart for the pencil lead example. Three key characteristics are being monitored on the same chart.
Group short run s chart: All three characteristics—break force (A), drag (B), and lead diameter (C)—appear to randomly fluctuate in the MAX and MIN positions. This indicates that the initial target s values were good estimators for all of the characteristics.
Group short run Xbar chart: It appears that all three key characteristics are randomly fluctuating in the MAX and MIN positions. This means that the initial target values were good estimators of the actual means for each of the three characteristics.
Group short run s chart: Continue using the initial target s values for all three characteristics. The charts may look good, but only the capability studies will determine if the characteristics are meeting engineering requirements.
Group short run Xbar chart: Continue using the initial target X values. No recalculation is necessary. The process averages appear stable and predictable. Continue to collect data. If the process remains stable, reduce sampling frequency.
Estimates of the process average should be calculated separately for each characteristic on each part on the group short run charts. The estimate of the process average for break force can be found in Calculation 1.
Calculation 1. Estimate of the process average for characteristic A, break force.
Estimates of sigma are also calculated separately for each characteristic on each part on the group short run charts. Continuing with characteristic A, see Calculations 2 and 3.
Calculation 2. s calculation for characteristic A, break force.
Calculation 3. Estimate of the process standard deviation for characteristic A, break force.
Calculations 4, 5, and 6 show the capability calculations for break force, characteristic A.
Calculation 4. Cp calculation for characteristic A, break force.
Calculation 5. Cpk upper for characteristic A, break force.
Calculation 6. Cpk lower calculation for characteristic A, break force.
Additional statistics and process capability and performance calculations for key characteristics B and C are shown in Table 4.
Table 4. Additional statistics and process capability and performance calculations for the drag and diameter key characteristics.
When you use SPC software from InfinityQS, consuming the information provided by group short run Xbar-s charts becomes faster and easier than ever. See how this type of analysis is surfaced in InfinityQS solutions.
FOOTNOTE: 1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.
Group target Xbar-s charts provide information about changes in process averages and the standard deviation across multiple measurement subgroups of similar characteristics that have a common process. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group target Xbar-s chart works.
Figure 1. Three hole-location measurements from a rocker.
The rocker shown in Figure 1 is machined from an iron casting. There have been complaints from field mechanics that the rockers are not interchangeable and that the holes do not always line up with mating parts. To monitor the uniformity of the hole locations, the operators would like to use a chart at the milling machine to track the variability of the three hole locations.
Because production volume is very high and all the measurements represent hole locations of different distances created on the same machine, a group target Xbar-s chart is selected. Ten rockers are measured every hour.
Table 1. Group target Xbar-s chart data collection sheet for three hole locations on a rocker. MAX and MIN plot points are shown in bold.
Figure 2. Group target Xbar-s chart representing three different hole locations on the same part.
Group s chart: Location a appears in the MAX position in every group. This indicates that location a has the largest standard deviation. Locations b and c appear randomly in the MIN position, meaning that location b and c’s standard deviation values are both similar to one another and smaller than location a’s.
Group target Xbar chart: The coded Xbar for location a appears in the MAX. position in every group and its value is always positive. This indicates that the average hole location at location a is consistently higher than the engineering nominal (target) value.
Location c appears in the MIN position in all nine groups and its value is always negative. This means that the average hole location distance at location c is consistently lower than its engineering nominal (target) value.
If all of the locations on the group target Xbar chart were behaving randomly, a single estimate of the process average could be used to estimate the process average for all locations. However in this case, the group target Xbar chart does not exhibit random behavior.
Given nonrandom patterns on a group target Xbar chart, estimates of the process average should be calculated separately for each characteristic or location. This is illustrated in Calculation 1 using data from hole location a.
Calculation 1. Estimate of the process average for hole location a.
Estimates of sigma are also calculated separately for each characteristic or location on the group target chart. Continuing with hole location a, see Calculations 2 and 3.
Calculation 2. Calculation of s for use in estimating the process standard deviation for hole location a.
Calculation 3. Estimate of the process standard deviation for hole location a.
The Cp and Cpk calculations for hole location a are shown in Calculations 4, 5, and 6.
Calculation 4. Cp calculation for hole location a.
Calculation 5. Cpk upper calculation for hole location a.
Calculation 6. Cpk lower calculation for hole location a.
The process capability and performance values for hole locations b and c are shown in Table 2.
Table 2. Summary statistics and process capability and performance ratios for hole locations b and c.
When you use SPC software from InfinityQS, consuming the information provided by group target Xbar-s charts becomes faster and easier than ever. See how this type of analysis is surfaced in InfinityQS solutions.
Group Xbar-s charts help you assess changes in averages and the standard deviation across measurement subgroups for a characteristic. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group Xbar-s chart works.
Figure 1. Three width measurements from a yoke.
This yoke is machined from an aluminum casting. There have been complaints from the assembly department that some of the yokes have a taper on the inside width. To monitor the uniformity of the inside widths, a group chart is set up at the milling machine to track the width at locations a, b, and c.
Because the production volume is very high, and the same characteristic is being measured at three different locations on the part, a group Xbar-s chart is selected. Ten yokes are measured every hour.
Table 1. Data collection sheet for the group Xbar-s chart. MAX and MIN plot points are shown in bold.
Figure 2. Group Xbar-s chart representing three different yoke width locations.
Group s chart: Location a appears in the MAX position for all groups. This suggests that location a has the largest standard deviation. Locations b and c appear randomly in the MIN position. This indicates that locations b and c have similar standard deviations and they are less than location a’s.
Group Xbar chart: The difference between the MAX and MIN for each group represents taper within the yokes. Locations a, b, and c appear randomly in the MAX position. However, location a appears five out of nine times in the MIN position. This might indicate that location a has a smaller diameter than either of the two other locations. However, this supposition is not as strong as it would be if location a represented the MIN position for all groups.
The repeated presence of location a in the MAX position in the group s chart may be the result of the inability of tooling to hold the work piece consistently during the manufacturing of the yokes. Notice that location a is found at the end of the yoke. This may signify the need for tooling changes that will hold the outer ends more rigidly during manufacturing.
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 yoke width at location a.
Estimates of sigma are also calculated separately for each characteristic or location on the group chart. Continuing with yoke width location a, see Calculations 2 and 3.
Calculation 2. Calculation of the average sample standard deviation for yoke width location a.
Calculation 3. Estimated standard deviation for yoke width location a.
Calculations 4, 5, and 6 show the process capability and performance calculations for yoke width location a.
Calculation 4. Cp calculation for width location a.
Calculation 5. Cpk upper calculation for width location a.
Calculation 6. Cpk lower calculation for width location a.
The process capability and performance ratio calculations for yoke widths at locations b and c are shown in Table 2.
Table 2. Summary statistics and process capability and performance ratios for yoke widths at locations b and c.
When you use SPC software from InfinityQS, consuming the information provided by group Xbar-s charts becomes faster and easier than ever. See how this type of analysis is surfaced in InfinityQS solutions.
Short run Xbar and s (Xbar-s) charts can help you identify changes in the averages and standard deviation of multiple characteristics in a limited production run. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a short run Xbar-s chart works.
Figure 1. Delta torque is a performance key characteristic on self-locking fastener systems.
Torque is tested on self-locking nuts using precision stud standards and production nuts. During production, the nuts are slightly deformed so that the threads create an interference or locking fit with the stud. The run-on torque is the average prevailing torque while turning the nut on the stud seven clockwise revolutions. The runoff torque is the maximum force it takes to turn the nut back off the stud one counterclockwise revolution. The delta torque is the run-on torque minus the run-off torque. Each fastening system has its own minimum delta torque requirements and the standard deviations are expected to vary from system to system.
Torque tests are performed for each batch of locking nuts. Ten samples are tested from each batch. To monitor the delta torque consistency, regardless of the nut/bolt locking system, a short run Xbar-s chart is selected. This is the appropriate chart because the subgroup sizes are large and the standard deviations are different from system to system.
Before a short run chart can be used, target values must first be defined.
System A has previously been maintained using traditional Xbar-s charts. On the most recent set of in-control charts, the centerline on the Xbar chart was 2.920. The centerline on the s chart was 0.089. Therefore, these centerlines are used as target values for system A.
Figure 2. Target values for locking system A.
The consistency of locking system B has never been evaluated with a control chart. However, quality assurance personnel have taken 28 delta torque measurements at some time in the past. Equation 15.14 was used to convert the sample standard deviation from those 28 measurements into the targets found in Figure 3.
Figure 3. Target values for locking system B.
Like system A, Rocking system C has previously been evaluated using traditional Xbar-s charts. On the most recent set of in-control charts, the centerline on the Xbar chart was 5.125. The centerline on the s chart was 0.337. Therefore, these centerlines are used as target values for system C (see Figure 4).
Figure 4. Target values for locking system C.
Table 1. Delta torque data sheet and plot point calculations.
Figure 5. Delta torque short run Xbar and s control charts for locking systems A, B, and C.
Short run s chart: If evaluating product-specific variation, locking system A’s delta torque seems to be behaving randomly. All eight of system B’s plot points fall above the centerline with one of them falling above the UCL. System C’s delta torque favors the high side with one plot point beyond the UCL. Overall, the process reveals a run of 9 plot points above the centerline that occur across three product lines (subgroups 13 through 20).
Short run Xbar chart: All seven of system A’s plot points fall below the centerline with three of them falling below the LCL. Seven of system B’s eight plot points are situated above the centerline with three above the UCL. System C appears to be behaving randomly. Looking at patterns across locking systems, there is a gradual decrease in the average from plot point 6 through 12. Also, it looks as though the average has shifted higher between plot points 13 and 20.
Short run s chart: The target s came from past control charts, therefore, the fact that the plot points are behaving randomly indicates that the standard deviation has not changed since data were last recorded.
Short run Xbar chart: The target X came from past charts, therefore, the run below the centerline indicates the delta torque has decreased since data were last recorded. This is an assignable cause and should be investigated. If the shift is found to be desirable, deliberate, and permanent, the target X should be recalculated based on system A’s current overall average. If the shift is found to be an unwanted condition, do not recalculate target X. Instead, eliminate the cause of the downward shift.
Short run s chart: The target s came from past quality assurance records. The run above the centerline, therefore, indicates that the standard deviation has significantly increased since data were last recorded. This may be an assignable cause and should be investigated. If the shift is found to be an unwanted condition, do not recalculate target s. Instead, eliminate the cause of the increased variability.
Short run Xbar chart: The target X came from quality assurance records, therefore, the run above the centerline indicates the delta torque has increased since data were last recorded. This may be an assignable cause and should be investigated. If this significant increase in delta torque is desirable, then the target X should be recalculated based on system B’s current overall average. If the shift is unwanted, do not recalculate target X. Instead, eliminate the assignable cause for the increase in the delta torque average.
Short run s chart: Because the target s was based on the centerline from an older, in-control s chart, the run above the centerline indicates that the process standard deviation has increased significantly since the last time the system C product was manufactured. This should be treated as an assignable cause because the target s is based upon actual data. If the increase in standard deviation for system C is expected to be a permanent change, then the target s should be recalculated based on the current overall average standard deviation (see Calculation 1). Otherwise, if the assignable cause is to be removed to reduce the current amount of variation, the old target s should be saved to represent the current expected level of variability.
Calculation 1. Recalculating locking system C’s target s based on current data from control chart. This is done only if the change in variability is expected to be a permanent one.
Short run Xbar chart: The target X has been obtained from a recent in-control chart, and the plot points are behaving randomly. This indicates that the initial target X was a good estimator of the actual delta torque. There is no need to recalculate system C’s target X.
Estimates of the process average should be calculated separately for each characteristic or part on short run Xbar-s charts. In this case, estimates of the process average should be calculated separately for each different locking system. Calculation 2 shows the calculation for the estimate of the overall average of locking system B.
Calculation 2. Estimate of the process average for locking system B.
Estimates of sigma are also calculated separately for each characteristic or location represented on short run Xbar-s charts. In this case, estimates of the process standard deviation should be calculated for each different locking system. Estimates of the process standard deviation for locking system B are found in Calculation 3.
Calculation 3. Calculation of s for locking system B based on current data from the short run s control chart.
Calculation 4. Calculation of the estimate of the process standard deviation for locking system B.
The Cpk lower calculation for locking system B is shown in Calculation 5. Because there is only a minimum specification, no Cp or Cpk upper value is calculated for locking system B.
Calculation 5. Cpk lower calculation for fastener system B delta torque.
Table 2. Additional summary statistics and process performance ratios for locking systems A and C.
When you use SPC software from InfinityQS, consuming the information provided by short run Xbar-s charts becomes faster and easier than ever. See how this type of analysis is surfaced in InfinityQS solutions.
See how the target Xbar-s chart enables plant-floor personnel to maintain tight tolerances on high-volume production lines.
Target Xbar and s (Xbar-s) charts can help you identify changes in the average and standard deviation of a characteristic. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a target Xbar-s chart works.
Figure 1. Rivet head height is a key characteristic. The measurement is taken with the aid of a gauge block.
Rivet head height is a key characteristic. The height is measured off a gauge block. If the height is too low, the installed rivet will recede below the surface. If it is too high, it will protrude. Either case requires rework and is unacceptable. Three different types of rivets are manufactured, each with different target head heights and tolerances. In this example, the target Xbar-s chart allows operators to maintain extremely tight tolerances for a high-volume, high-speed production process.
This example provides a deep dive into the manual calculations behind the target Xbar-s chart. InfinityQS® solutions—ProFicient™ and Enact®—automate chart creation and help you optimize processes faster.
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Table 1. Target head heights and specifications.
Several rivet types are to be plotted on the same chart, but because only one characteristic, head height, is to be controlled, use of a target chart would be appropriate. The production volume is extremely high (thousands per hour), the data collection is quick, and the analysis is being done with the assistance of computer software. For all these reasons, a target Xbar-s chart is selected.
To determine how often measurements should be taken, a header mechanic is surveyed. It is revealed that adjustments to the equipment affecting head height are made about every hour. To capture the effects of these adjustments, samples of 10 are taken every 10 minutes.
Table 2. Data collection sheet for three different rivet head heights.
Figure 2. Head height target Xbar-s control chart.
Calculation 1. Calculations for target Xbar chart.
Calculation 2. Calculations for s chart.
s chart: The chart is in control. This shows that the sample standard deviations of head heights for all three rivet types are similar.
Target Xbar chart: This chart is also in control. There are no indications of assignable causes. This means that the difference between the average head heights of all three rivet types and their respective targets is about the same.
Because the target Xbar chart is in control, the process average for all rivet types can be estimated using the coded X.
Calculation 3. Estimate for the coded overall process average rivet head height (to be used in Cpk calculations for all three rivet types).
Because the s chart is in control, the process standard deviation can be estimated for all three rivet types using the formula found in Calculation 4.
Calculation 4. Estimating sigma using s.
These ratios are calculated using coded data. The coded nominal for the head height characteristic is zero. Therefore, for rivet A, the coded USL is +10 and the coded LSL is –10. Following are calculations for the rivet A head height.
Calculation 5. Cp calculation for rivet A head height.
Calculation 6. Cpk upper calculation for rivet A head height.
Calculation 7. Cpk lower calculation for rivet A head height.
Table 3. Cp and Cpk calculations for B and C rivets.
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