Improve Productivity with SPC
Inefficiency is the enemy of manufacturing profit.
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How SPC Can Help
“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—
- Reduce scrap and rework
- Minimize unplanned downtime
- Provide input or guidance for best practices
- Improve product consistency
Use Enact to Improve Efficiency and Productivity
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.
The Second Life of Data: Quality Analytics and Manufacturing Efficiency
Reduce Defects and Recalls
Non-conforming product can ruin your day, your reputation—and your manufacturing business.
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How SPC Can Help
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:
- Product and material replacement costs
- Transportation costs
- Wasted employee hours
- Lost production time
- Loss of brand reputation
- Loss of customers
Use Enact to Reduce Defects and Recalls
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.
How to Reduce Waste in Manufacturing
Out-of-spec product can rack up losses. SPC enables waste management in manufacturing.
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Reduce Waste and Scrap: SPC Can Help
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.
Use Enact to Enable Waste Management in Manufacturing
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.
New SPC Tools for a New Era of Quality
Discover substantial benefits for your manufacturing organization when you modernize shop floor operations with new quality control tools and techniques.
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Embrace a better SPC solution
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.
Think you can’t afford an SPC solution?
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.
- Starts at just $65/license/month
- Easy to learn and use from anywhere, anytime
- Cloud-based deployment and extensive self-help to reduce IT burden
- Supplemental training available onsite or at our training facilities
The cost of standing still
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.
Easy to start. Easy to expand.
Enact empowers you to quickly realize the benefits of digital data collection and analysis. Start today with:
- Five Enact licenses: add more as needed
- Quick Setup wizard: your guide to configuring data collections
- Video tutorials and easy-to-use help: available in our Guided Learning Center
- Flexible expansion: reconfigure your licenses, add licenses, integrate with other manufacturing systems, and move to automated data collection—at any time
Mitigate Risk
Prioritize quality and process control to reduce regulatory compliance risks, customer complaints, and recalls.
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Prioritize Quality and Process Optimization to Protect Your Brand
InfinityQS® solutions use proven statistical process control (SPC) methodology to help you prevent problems—and the associated risks.
Boost ROI
From giving you the insight you need to monitor supplier quality to improving traceability and streamlining audits, InfinityQS solutions provide unbeatable ROI.
Protect brand equity
Consistency is a hallmark of brand equity. How can you ensure that customers get the same high-quality product from any manufacturing site, at any time? How can you detect potential quality problems as quickly as possible—or better yet, spot the warning signs and prevent the problems? InfinityQS solutions provide targeted yet extensive data collection and capabilities, automated alerts, and aggregated access to historical data so that you can produce a consistently excellent product that meets brand expectations.
Reduce customer complaints
Your customers demand high quality, reliable products. You need proven, efficient quality control methods to meet those demands. One faulty process can set back both production and customer loyalty. With InfinityQS, you get solutions that help you respond to customer needs—quickly, flexibly, and consistently.
Minimize recalls
Product recalls are costly, not just in lost time and wasted materials but also in the potential loss of customer confidence and brand reputation. InfinityQS gives you the insight you need to reduce defect levels, automate policy and procedure enforcement, and reduce scrap and rework—all of which can help to prevent the dreaded recall.
Measurable Results
Hundreds of InfinityQS clients responded to a survey we conducted, documenting savings in key metrics including scrap, rework, defects, cycle time, overtime, warranty claims, MRB/sorting, holds, escapes, data collection, reporting and recalls.
The average results are as follows:
- 12.7% Weekly Scrap Reduction
- 14.3% Man-hour Rework Reduction
- 14.1% Overtime Reduction
- 12.9% Defect Cost Reduction
- 13.6% Cycle Time Reduction
- 14.1% Warranty Claim Reduction
- 11.5% MRB/Sorting Reduction
- 12.5% Holds Reduction
- 10.7% Escapes Reduction
- 14.4% Data Collection Time Reduction
- 17.1% Report Time Reduction
Elevating Quality to the Top Floor
Easy to start. Easy to expand.
Enact empowers you to quickly realize the benefits of digital data collection and analysis. Start today with:
- Five Enact licenses: add more as needed
- Quick Setup wizard: your guide to configuring data collections
- Video tutorials and easy-to-use help: available in our Guided Learning Center
- Flexible expansion: reconfigure your licenses, add licenses, integrate with other manufacturing systems, and move to automated data collection—at any time
Ensure Product & Quality Compliance
Simplify compliance, streamline audits, and meet or exceed industry quality control standards, thanks to InfinityQS built-in features.
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Improve Product Quality & Consistency while Meeting Compliance Requirements
Whether you need to comply with government regulations, meet customer specifications, or simply aim to exceed industry quality control standards, InfinityQS® solutions include built-in features to make your work easier.
Meet Lean and Six Sigma requirements
Process improvement methodologies like Six Sigma and Lean Manufacturing rely on solid data-collection plans and operational insight. InfinityQS gives you the ability to collect, aggregate, and analyze process and quality data to meet the demands of such programs.
Improve traceability and reduce recall risk
The ability to find any part or focus in on any process is a must for reliable traceability—and in turn, can help to prevent or reduce recalls. But how can you expect agile, flexible responses to data queries when half the work of gathering or locating data is still being done on clipboards and in spreadsheets? InfinityQS solves this problem with automated, responsive capabilities that simplify collecting, aggregating, and analyzing data, enabling you to find the information you need, easily and swiftly.
Simplify audits
InfinityQS quality and process optimization solutions provide automated, customizable, enterprise-wide quality- and process-data collection, analysis, and reporting so you can keep production moving and satisfy compliance and auditing demands. Keep throughput high and information at your fingertips.
Comply with regulations
In today’s global market, you must juggle the details of multiple national and international regulations and compliance requirements. Meeting those expectations—and managing the reporting and downtime associated with audits and recalls—can drain time, energy, and resources. With InfinityQS, get automated notification when compliance checks are—or aren’t—performed and visibility into potential or actual failures.
Ensure specification compliance
InfinityQS is ISO Certified 9001/2001, so you can have confidence in both quality and security controls.
Electrical Devices
Easy to start. Easy to expand.
Enact empowers you to quickly realize the benefits of digital data collection and analysis. Start today with:
- Five Enact licenses: add more as needed
- Quick Setup wizard: your guide to configuring data collections
- Video tutorials and easy-to-use help: available in our Guided Learning Center
- Flexible expansion: reconfigure your licenses, add licenses, integrate with other manufacturing systems, and move to automated data collection—at any time
Xbar and s (Xbar-s) Chart
In high-speed operations with large sample sizes and automated data collections, use this chart to maintain consistency of key characteristics.
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What are the Components of the Xbar-s Chart?
The Xbar chart (the upper chart in this figure) plots the average of individual values in a subgroup (i.e., the subgroup mean). The 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.
Xbar-s Charts for a Single Characteristic
For example, this sample chart (taken from InfinityQS® ProFicient™ software) highlights subgroup 9 of 20 subgroups. You can see that the average of the subgroup’s plot points is 34.02 (top chart) and the standard deviation is 2.755 (lower chart).
Scroll down to learn how to use this chart.
Automate and Simplify Control Chart Analysis
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How to Use the Xbar-s Chart
Use the Xbar-s chart chart when your sample size is 10 or more (n≥10). This scenario is most common when a lot of data is available (or necessary) and the data acquisition cost is low.
For example, you might use this chart for data taken from Programmable Logic Controllers (PLCs) or other automated data-collection devices. Injection molding, multihead fill operations, and continuous high-speed production lines on which many measurements can be gathered quickly and affordably are all good environments for this type of chart.
Each of the special use case examples described on this page presume a large sample size (i.e., 10 or more).
Advantages and Disadvantages of Using the Xbar-s Chart
Advantages
- Very sensitive to small changes in the subgroup mean
- Standard deviation is usually a more accurate indicator of process variation than is the range
Disadvantages
- Requires gathering large amounts of data to calculate control limits
Decision Tree
Use the following decision tree to determine whether the Xbar-s chart is the best choice.
Scroll down to see special use examples.
Special Uses
Today, control charts are a key tool for quality control and figure prominently in Lean manufacturing and Six Sigma efforts.
Target Xbar-s Chart
- Plot multiple parts or characteristics with similar variability on the same chart.
- Assess statistical control for the process as well as for each of its parts or characteristics.
- Detect very small process shifts.
- Directly plot data from gauges that are zeroed out on target values (no data transformation or coding necessary).
Short Run Xbar-s Chart
Short run charts are used for short production runs. The short run Xbar-s chart can help you identify changes in the averages and standard deviation of multiple characteristics, even those with different nominals, units of measure, or standard deviations.
- Summarize a great amount of data while still detecting small changes in process average.
- Detect the difference between process- and product-specific variabilities.
- Plot variations of multiple products, even those with differing standard deviations, nominals, or units of measure—all on one chart.
Group Xbar-s Chart
Group charts display several parameters, characteristics, or process streams on one chart. Group Xbar-s charts help you assess changes in averages and the standard deviation across measurement subgroups for a characteristic.
- Compare the variations of a variety of products or characteristics.
- See the difference between variations that are caused by changes in average and those caused by changes in the standard deviation.
- Clearly detect characteristics that are priorities for attention.
Group Target Xbar-s Chart
The group target Xbar-s chart provides information about changes in process averages and the standard deviation across multiple measurement subgroups of similar characteristics that have a common process. Part numbers and engineering nominal values can differ across these characteristics.
- Compare variations of multiple products or characteristics as well as similar characteristics with different averages.
- See the difference between variations that are caused by changes in average and those caused by changes in the standard deviation.
Group Short Run Xbar-s Chart
The group short run Xbar-s chart enables you to spot changes in the process average and standard deviation across multiple characteristics in a short run environment.
- Identify the difference between process- and product-specific variations.
- Compare variations of multiple products or characteristics.
- Analyze characteristics from a variety of parts, even those with different means, standard deviations, or units of measure.
- See the difference between variations that are caused by changes in average and those caused by changes in the standard deviation.
Group Short Run Xbar-s Chart Example
Group Short Run Xbar-s Charts
Group short run Xbar-s charts enable you to spot changes in the process average and standard deviation across multiple characteristics in a limited production run. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group short run Xbar-s chart works.
Figure 1. Mechanical pencil with three key characteristics.
Case Description
A company manufactures mechanical pencil lead. There are three key characteristics (see Table 30.5).
- Break force—The amount of pressure it takes to break the lead (extended 1.5 mm) at a 38° angle with the force applied 3 cm from the lead rip
- Drag—A proprietary measure of how smoothly the lead releases onto a given paper
- Diameter—The diameter of the lead
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.
Sampling Strategy
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.
Target Values
Preliminary tests on all three key characteristics were conducted. The purpose of the tests was to establish target values for the group short run charts to be used. The target values are found in Table 2.
Table 2. Target X and target s values for the three mechanical pencil lead key characteristics.
Data Collection Sheet
Table 3. Data collection sheet for the group short run Xbar-s chart pencil lead example. MAX and MIN plot points are shown in bold.
Group Short Run Xbar-s Chart
Figure 2. Group short run Xbar-s chart for the pencil lead example. Three key characteristics are being monitored on the same chart.
Chart Interpretation
Group short run s chart: All three characteristics—break force (A), drag (B), and lead diameter (C)—appear to randomly fluctuate in the MAX and MIN positions. This indicates that the initial target 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.
Recommendations
Group short run s chart: Continue using the initial target s values for all three characteristics. The charts may look good, but only the capability studies will determine if the characteristics are meeting engineering requirements.
Group short run Xbar chart: Continue using the initial target X values. No recalculation is necessary. The process averages appear stable and predictable. Continue to collect data. If the process remains stable, reduce sampling frequency.
Estimating the Process Average
Estimates of the process average should be calculated separately for each characteristic on each part on the group short run charts. The estimate of the process average for break force can be found in Calculation 1.
Calculation 1. Estimate of the process average for characteristic A, break force.
Estimating Sigma
Estimates of sigma are also calculated separately for each characteristic on each part on the group short run charts. Continuing with characteristic A, see Calculations 2 and 3.
Calculation 2. s calculation for characteristic A, break force.
Calculation 3. Estimate of the process standard deviation for characteristic A, break force.
Calculating Process Capability and Performance Ratios
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.
Group Short Run Xbar-s Chart Advantages
- Graphically illustrates the variation of multiple product or process characteristics relative to each other.
- Characteristics from different parts with different means, different standard deviations, and different units of measure can all be analyzed on the same chart.
- Separates variation due to changes in the average from variation due to changes in the standard deviation.
- Separates variation due to the process from variation that is product specific.
Group Short Run Xbar-s Chart Disadvantages
- No visibility of characteristics that fall between the MAX and MIN plot points
- Cannot detect certain nonrandom conditions because the group charts described here have no control limits
- Lots of calculations
An Additional Comment About the Case
Additional statistics and process capability and performance calculations for key characteristics B and C are shown in Table 4.
Table 4. Additional statistics and process capability and performance calculations for the drag and diameter key characteristics.
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 Chart Example
Group Target Xbar-s Charts
Group target Xbar-s charts provide information about changes in process averages and the standard deviation across multiple measurement subgroups of similar characteristics that have a common process. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group target Xbar-s chart works.
Figure 1. Three hole-location measurements from a rocker.
Case Description
The rocker shown in Figure 1 is machined from an iron casting. There have been complaints from field mechanics that the rockers are not interchangeable and that the holes do not always line up with mating parts. To monitor the uniformity of the hole locations, the operators would like to use a chart at the milling machine to track the variability of the three hole locations.
Sampling Strategy
Because production volume is very high and all the measurements represent hole locations of different distances created on the same machine, a group target Xbar-s chart is selected. Ten rockers are measured every hour.
Data Collection Sheet
Table 1. Group target Xbar-s chart data collection sheet for three hole locations on a rocker. MAX and MIN plot points are shown in bold.
Group Target Xbar-s Chart
Figure 2. Group target Xbar-s chart representing three different hole locations on the same part.
Chart Interpretation
Group s chart: Location a appears in the MAX position in every group. This indicates that location a has the largest standard deviation. Locations b and c appear randomly in the MIN position, meaning that location b and c’s standard deviation values are both similar to one another and smaller than location a’s.
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.
Recommendations
- The group target Xbar chart reveals two consistent problems: Location a is always wider than target, and location c is always closer. This type of problem is fixed by changing the location of one or more holes during the job setup. The chart itself does not indicate which hole to relocate. A logical place to begin investigation is with hole 1 because its location affects both key locations a and c.
- Looking at the group s chart, the distance between holes 1 and 3 (hole location a) varies more than the other hole relationships. This also means there is excess variation in the horizontal axis. Operators should verify this assumption with process engineers and remedy the problem..
Estimating the Process Average
If all of the locations on the group target Xbar chart were behaving randomly, a single estimate of the process average could be used to estimate the process average for all locations. However in this case, the group target Xbar chart does not exhibit random behavior.
Given nonrandom patterns on a group target Xbar chart, estimates of the process average should be calculated separately for each characteristic or location. This is illustrated in Calculation 1 using data from hole location a.
Calculation 1. Estimate of the process average for hole location a.
Estimating Sigma
Estimates of sigma are also calculated separately for each characteristic or location on the group target chart. Continuing with hole location a, see Calculations 2 and 3.
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.
Calculating Process Capability and Performance Ratios
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.
Group Target Xbar-s Chart Advantages
- Simultaneously illustrates the variation of multiple product or process characteristics.
- Similar characteristics with different averages can be analyzed on the same chart.
- Separates variation due to changes in the average from variation due to changes in the standard deviation.
- Multiple characteristics can be tracked on one chart.
Group Target Xbar-s Chart Disadvantages
- No visibility of the characteristics that fall between the MAX and MIN plot points.
- The use of negative numbers can be confusing.
- Cannot detect certain nonrandom conditions because the group target charts described here have no control limits.
An Additional Comment About the Case
The process capability and performance values for hole locations b and c are shown in Table 2.
Table 2. Summary statistics and process capability and performance ratios for hole locations 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.
FOOTNOTE:
1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.
Group Xbar-s Chart Example
Group Xbar-s Charts
Group Xbar-s charts help you assess changes in averages and the standard deviation across measurement subgroups for a characteristic. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group Xbar-s chart works.
Figure 1. Three width measurements from a yoke.
Case Description
This yoke is machined from an aluminum casting. There have been complaints from the assembly department that some of the yokes have a taper on the inside width. To monitor the uniformity of the inside widths, a group chart is set up at the milling machine to track the width at locations a, b, and c.
Sampling Strategy
Because the production volume is very high, and the same characteristic is being measured at three different locations on the part, a group Xbar-s chart is selected. Ten yokes are measured every hour.
Data Collection Sheet
Table 1. Data collection sheet for the group Xbar-s chart. MAX and MIN plot points are shown in bold.
Group Xbar-s Chart
Figure 2. Group Xbar-s chart representing three different yoke width locations.
Chart Interpretation
Group s chart: Location a appears in the MAX position for all groups. This suggests that location a has the largest standard deviation. Locations b and c appear randomly in the MIN position. This indicates that locations b and c have similar standard deviations and they are less than location a’s.
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.
Recommendation
The repeated presence of location a in the MAX position in the group s chart may be the result of the inability of tooling to hold the work piece consistently during the manufacturing of the yokes. Notice that location a is found at the end of the yoke. This may signify the need for tooling changes that will hold the outer ends more rigidly during manufacturing.
Estimating the Process Average
Process average estimates should be performed separately for each characteristic or location on the group chart (see Calculation 1).
Calculation 1. Estimate of the process average for yoke width at location a.
Estimating Sigma
Estimates of sigma are also calculated separately for each characteristic or location on the group chart. Continuing with yoke width location a, see Calculations 2 and 3.
Calculation 2. Calculation of the average sample standard deviation for yoke width location a.
Calculation 3. Estimated standard deviation for yoke width location a.
Calculating Process Capability and Performance Ratios
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.
Group Xbar-s Chart Advantages
- Graphically illustrates the variation of multiple product or process characteristics simultaneously and relative to each other.
- Pinpoints the characteristics that are in need of the most attention.
- Separates variation due to changes in the average from variation due to changes in the standard deviation.
- Multiple measurement locations can be tracked on one chart.
Group Xbar-s Chart Disadvantages
- No visibility of the characteristics that fall between the MAX and MIN plot points.
- Cannot detect certain out-of-control conditions because the group charts described here have no control limits.
- Given the large amounts of data used in s charts, efficient analysis typically requires software.
An Additional Comment About the Case
The process capability and performance ratio calculations for yoke widths at locations b and 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.
FOOTNOTE:
1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.
Short Run Xbar-s Chart Example
Short Run Xbar-s Charts
Short run Xbar and s (Xbar-s) charts can help you identify changes in the averages and standard deviation of multiple characteristics in a limited production run. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a short run Xbar-s chart works.
Figure 1. Delta torque is a performance key characteristic on self-locking fastener systems.
Case Description
Torque is tested on self-locking nuts using precision stud standards and production nuts. During production, the nuts are slightly deformed so that the threads create an interference or locking fit with the stud. The run-on torque is the average prevailing torque while turning the nut on the stud seven clockwise revolutions. The runoff torque is the maximum force it takes to turn the nut back off the stud one counterclockwise revolution. The delta torque is the run-on torque minus the run-off torque. Each fastening system has its own minimum delta torque requirements and the standard deviations are expected to vary from system to system.
Sampling Strategy
Torque tests are performed for each batch of locking nuts. Ten samples are tested from each batch. To monitor the delta torque consistency, regardless of the nut/bolt locking system, a short run Xbar-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.
Target Values
Before a short run chart can be used, target values must first be defined.
Locking System A
System A has previously been maintained using traditional Xbar-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.
Locking System B
The consistency of locking system B has never been evaluated with a control chart. However, quality assurance personnel have taken 28 delta torque measurements at some time in the past. Equation 15.14 was used to convert the sample standard deviation from those 28 measurements into the targets found in Figure 3.
Figure 3. Target values for locking system B.
Locking System C
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.
Data Collection Sheet
Table 1. Delta torque data sheet and plot point calculations.
Short Run Xbar-s Chart
Figure 5. Delta torque short run Xbar and s control charts for locking systems A, B, and C.
Chart Interpretation
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.
Recommendations
Locking System A
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.
Locking System B
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.
Locking System C
Short run s chart: Because the target s was based on the centerline from an older, in-control s chart, the run above the centerline indicates that the process standard deviation has increased significantly since the last time the system C product was manufactured. This should be treated as an assignable cause because the target 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.
Estimating the Process Average
Estimates of the process average should be calculated separately for each characteristic or part on short run Xbar-s charts. In this case, estimates of the process average should be calculated separately for each different locking system. Calculation 2 shows the calculation for the estimate of the overall average of locking system B.
Calculation 2. Estimate of the process average for locking system B.
Estimating Sigma
Estimates of sigma are also calculated separately for each characteristic or location represented on short run Xbar-s charts. In this case, estimates of the process standard deviation should be calculated for each different locking system. Estimates of the process standard deviation for locking system B are found in Calculation 3.
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.
Calculating Process Capability and Performance Ratios
The Cpk lower calculation for locking system B is shown in Calculation 5. Because there is only a minimum specification, no Cp or Cpk upper value is calculated for locking system B.
Calculation 5. Cpk lower calculation for fastener system B delta torque.
Short Run Xbar-s Chart Advantages
- Graphically illustrates the variation of multiple products with different nominals, different standard deviations, and even different units of measure all on the same chart.
- Separates sources of process variability from sources of product variability.
- Due to the large sample sizes, the short run Xbar chart is sensitive to small changes in the process average.
- Summaries large amounts of data.
Short Run Xbar-s Chart Disadvantages
- Requires software to effectively handle large amounts of data.
- The use of negative numbers and unitless ratios may be confusing at first.
- X, s, and process standard deviation estimates must be calculated separately for each characteristic represented on the chart.
Additional Comments About the Case
- The process capability and performance ratio calculations for locking systems A and C are found in Table 2.
- Summary statistics and Cpk lower values for systems A and C are based on the actual data from the data collection sheet (Table 1). In addition, no Cp or Cpk upper values are found in Table 2 because the locking systems all have one-sided specifications.
Table 2. Additional summary statistics and process performance ratios for locking systems A and C.
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.
FOOTNOTE:
1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.
Using the Target Xbar-s Chart: Example
See how the target Xbar-s chart enables plant-floor personnel to maintain tight tolerances on high-volume production lines.
How Do You Use Target Xbar-s Charts?
Target Xbar and s (Xbar-s) charts can help you identify changes in the average and standard deviation of a characteristic. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a target Xbar-s chart works.
Figure 1. Rivet head height is a key characteristic. The measurement is taken with the aid of a gauge block.
Case Description
Rivet head height is a key characteristic. The height is measured off a gauge block. If the height is too low, the installed rivet will recede below the surface. If it is too high, it will protrude. Either case requires rework and is unacceptable. Three different types of rivets are manufactured, each with different target head heights and tolerances. In this example, the target Xbar-s chart allows operators to maintain extremely tight tolerances for a high-volume, high-speed production process.
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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.
Sampling Strategy
Several rivet types are to be plotted on the same chart, but because only one characteristic, head height, is to be controlled, use of a target chart would be appropriate. The production volume is extremely high (thousands per hour), the data collection is quick, and the analysis is being done with the assistance of computer software. For all these reasons, a target Xbar-s chart is selected.
To determine how often measurements should be taken, a header mechanic is surveyed. It is revealed that adjustments to the equipment affecting head height are made about every hour. To capture the effects of these adjustments, samples of 10 are taken every 10 minutes.
Data Collection Sheet
Table 2. Data collection sheet for three different rivet head heights.
Target Xbar-s Chart
Figure 2. Head height target Xbar-s control chart.
Control Limit Calculations
Calculation 1. Calculations for target Xbar chart.
Calculation 2. Calculations for s chart.
Chart Interpretation
s chart: The chart is in control. This shows that the sample standard deviations of head heights for all three rivet types are similar.
Target Xbar chart: This chart is also in control. There are no indications of assignable causes. This means that the difference between the average head heights of all three rivet types and their respective targets is about the same.
Recommendations
- Based on the target Xbar chart, the process is running very close to target regardless of rivet type. This is a situation where the process should not be adjusted.
- Even though the standard deviations are similar for all three rivet types, one will still need to calculate separate Cp and Cpk ratios. This is necessary because the engineering tolerances are different for each rivet type.
Estimating the Process Average
Because the target Xbar chart is in control, the process average for all rivet types can be estimated using the coded X.
Calculation 3. Estimate for the coded overall process average rivet head height (to be used in Cpk calculations for all three rivet types).
Estimating Sigma
Because the s chart is in control, the process standard deviation can be estimated for all three rivet types using the formula found in Calculation 4.
Calculation 4. Estimating sigma using s.
Calculating Process Capability and Performance Ratios
These ratios are calculated using coded data. The coded nominal for the head height characteristic is zero. Therefore, for rivet A, the coded USL is +10 and the coded LSL is –10. Following are calculations for the rivet A head height.
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.
Target Xbar-s Chart Advantages
- Multiple parts or characteristics can be plotted on the same chart (provided they all exhibit similar variability).
- Data from gauges that are zeroed out on their target values can be plotted directly on the target Xbar without data coding or data transformation.
- Statistical control can be assessed for both the process and each unique part and/or characteristic being made in the process.
- Due to the large subgroup size, the Xbar chart is very sensitive to small process shifts.
Target Xbar-s Chart Disadvantages
- Requires software to efficiently handle the large amounts of data.
- The use of coded negative numbers can sometimes be confusing.
- When interpreting the target Xbar chart, both the zero line and the coded X must be taken into account. This accounts for some added complexity when interpreting the chart.
Additional Comments About the Case
- Process capability and performance calculations for the B and C rivets are shown in Table 3.
- Because the target Xbar-s chart proved to be in control, the only values that change when calculating the capability ratios are the specification limits. The coded X and sigma values used to calculate Cp and Cpk ratios are the same for all three rivet types.
Table 3. Cp and Cpk calculations for B and C rivets.
1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.
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Extend and Empower Your Quality Team
In modern manufacturing organizations, quality professionals seek to tightly manage every step in every process to ensure consistent quality—a task that becomes more challenging as production lines cross staff, processes, and plants.
Using statistical process control (SPC) for quality improvement can alleviate some of the complexity. SPC brings a systematic approach to data collection and analyses, no matter where they occur. Quality team leaders set the expectations for data collection (i.e., what, when, and how), and establish acceptable deviations. Unfortunately, traditional quality control in manufacturing ends there. The value of that data is often limited to a single use, verification of compliance, or an adjustment justification.
A central data repository extends the benefits of SPC by making the quality data you collect accessible throughout the organization, whether that’s on the plant floor or in the executive board room. With a single repository for quality data, commonly “siloed” information comes together to create a singular, company-wide picture of quality.
Making quality data consistent, accessible, and actionable empowers every team member to put quality first.
Get Everyone on the Quality Team
Standardization and centralization of data establishes a common language—and expectation—surrounding quality that cascades throughout the organization. When every team member is using the same playbook, some of the complexity dissipates. In its place, manufacturing organizations can introduce ways to improve quality and productivity.
Quality-focused teams can realize greater benefits from their statistical process control efforts.
Eliminate error-prone processes
Manual data collection can lead to “garbage in, garbage out,” wasting the time and resources it takes to collect and analyze the data. Handwritten data can be difficult to interpret, and paper reports can become lost or damaged. If data is missing or indecipherable during an audit, the results can be costly.
InfinityQS solutions enable semi-automated and automated data collection, as well as automated alerts and notifications, to ensure checks are completed and data is accurate. And centralizing your data in a single repository helps you build a clear picture of quality across the organization.
Empower real-time decision-making
Siloed data leads to slower decision-making. In contrast, InfinityQS quality improvement solutions make it easy for you to access data in real time—by production line, plant, or region—at the same pace you need to make quality decisions. Operations managers and quality team members know the moment an issue arises so they can take steps to preserve quality or avoid costly missteps.
Plan more efficiently
With a centralized data repository, empowered users can create and pull reports when they need them, without waiting for IT to merge data from multiple systems or manage a massive export. With accurate and complete data, you can easily plot a continuous improvement journey.
Identify high-impact quality improvements
With accessible, data-backed insights, quality teams can find the most influential quality initiatives to undertake as a company—by region, product, or plant. InfinityQS solutions help you spot transformative opportunities that might otherwise be buried in spreadsheets or stuck in an operational silo. And purpose-built analytical tools help you determine which initiatives will deliver the biggest and fastest ROI.
Save valuable time and money
Quality control in manufacturing is intended to save time and money—not drain resources or become just one more cost center. Quality management software solutions from InfinityQS help your whole quality team increase profits by improving some of the costliest manufacturing metrics like scrap and rework, unplanned downtime, overtime, defect costs, and warranty claims.
Empowered Quality Teams Improve Manufacturing Quality
Ready to empower every team member to put quality first? Take a peek at the features, analytics, dashboards, and reports in InfinityQS software to see how you can improve quality using data you already have.
Connect Your Teams, Improve Your Quality
Putting actionable information into the hands of every empowered team member—from operators to quality professionals to executive leaders—prevents quality disruptions and moves the organization toward quality manufacturing best practices. Working together, you can achieve stronger quality outcomes that transform the entire enterprise, such as:
- Optimized production
- Cost, defect, and recall reduction
- Reduced risk and downtime
- Improved product compliance and lower audit costs
- Better yields at the process, plant, regional, and enterprise levels
InfinityQS quality improvement solutions bring data and people together throughout the manufacturing process. The result is greater efficiency, better product consistency, and overall higher manufacturing quality.
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Quality Metrics
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Manufacturing Excellence Starts with the Data You Already Have
Modern manufacturers have two choices: to simply meet quality and regulatory standards or to pursue manufacturing excellence and reset the bar. Which do you choose?
The insight you need to break through quality barriers and transform your manufacturing organization is within reach. It’s in your quality metrics.
The metrics you measure are more than just report cards and to-do lists. They can help you adapt, thrive, and thrill customers with reliably high quality. The challenge is being able to see into that vast amount of data to determine which quality initiatives should rise to the top.
The key is to standardize and centralize your quality data in a single repository. Once performance data from different quality systems are unified, they can be turned into manufacturing intelligence.
Stop solving problems and start pursuing excellence. Use quality metrics to launch a perpetual cycle of continuous improvement.
Get the Total Quality Picture
What would happen if you only read 2% of your emails? You’d miss a lot.
That’s exactly what many manufacturing organizations are doing with their collected data; they dig deep into exception data and ignore the majority of their quality metrics. By doing so, they miss opportunities to make substantive, system-wide improvements.
InfinityQS quality improvement software aggregates a variety of quality metrics—and yes, this includes in-spec data, so it’s easy to compare performance across lines, parts, plants, and other key factors. Whether data are collected manually or through automation, they all flow into one place. Then the data are standardized so access to the information and analysis becomes easy, and you can see the “big picture” of quality across the organization.
Statistical process control (SPC)-driven dashboards and control charts bring quality priorities into focus. With access to this clarified data in real time, your busy executives can identify opportunities for huge improvements in quality, customer satisfaction, and profitability.
Better Decisions Lead to Better Quality
InfinityQS solutions help leaders model process capability so they can evaluate the impacts of quality improvement initiatives—and prioritize those that will have the most value.
Data stream grading, for example, enables executives to visually expose and isolate those areas of potential improvements. All streams of data are given a score based on actual performance versus expected performance, giving leaders a clear picture of what’s working, where they need to deploy Six Sigma support, and what they stand to gain.
Simple color-coded matrices show leaders where to capture “quick wins” and which processes will deliver transformational improvement.
With detailed metrics at their fingertips, executives gain visibility across the entire enterprise. Quality excellence that’s achieved in one plant or line can be replicated across the organization to maximize the impact and multiply return on investment (ROI). Even with limited resources, quality manufacturing leaders can turn data into intelligence and better-informed decisions.
Which Quality Metrics Matter Most?
All of your quality metrics matter—not just the defects or “lessons learned.” InfinityQS quality improvement solutions collect and combine all of your quality data into a single system so you can compare and improve performance across the enterprise. See what’s happening in your organization in real time and over time.
See What’s Ahead to Stay Ahead
InfinityQS helps manufacturers prevent quality issues rather than simply respond to them. Built to support quality manufacturing with real-time SPC, InfinityQS software gives leaders the information they need to predict quality outcomes, when and where they need it.
Dashboards transform key quality data into digestible summaries, so quality leaders can take proactive steps to reduce risk, increase efficiency, improve profitability, and produce top-quality products.
In modern manufacturing, it’s not enough to know what happened yesterday. To achieve quality excellence, you need to know what’s happening right now, what will happen if you take action, and where to begin.
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- Free 20-minute call with a product expert
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