A Practical Guide To Selecting The Right Control Chart
A Practical Guide to Selectingthe Right Control ChartInfinityQS International, Inc. 12601 Fair Lakes Circle Suite 250 Fairfax, VA 22033 www.infinityqs.com
A Practical Guide to Selecting the Right Control ChartIntroductionControl charts were invented in the 1920’s by Dr. Walter Shewhart as a visual toolto determine if a manufacturing process is in statistical control. If the control chartindicates the manufacturing process is not in control, then corrections or changesshould be made to the process parameters to ensure process and productconsistency. For manufacturers, control charts are typically the first indication thatsomething can be improved and warrants a root cause analysis or other processimprovement investigation. Today, control charts are a key tool for quality control andfigure prominently in lean manufacturing and Six Sigma efforts.Variables Data –Measurements taken on aWith over 300 types of control charts available, selecting the most appropriate onefor a given situation can be overwhelming. You may be using only one or two types ofcharts for all your manufacturing process data simply because you haven’t exploredfurther possibilities or aren’t sure when to use others. Choosing the wrong type ofcontrol chart may result in “false positives” because the chart may not be sensitiveenough for your process. Or there may be ways to analyze parts and processes youthought weren’t possible, resulting in new insights for possible process improvements.continuous scale such astime, weight, length, height,temperature, pressure, etc.These measurements canhave decimals.Attribute Data –Measurements takenThis guide leads quality practitioners through a simple decision tree to select the rightcontrol chart to improve manufacturing processes and product quality. This guidefocuses on variables data, not attribute data, and highlights powerful chartingfunctionality that users often overlook. You will learn which control chart is best fora given situation. InfinityQS’ ProFicient software offers easy setup and display of awide variety of control charts including the ones highlighted throughout this guide. Inaddition, ProFicient’s quality hub gathers data from disparate sources, across multipleplants or production lines, using automated or manual sampling to present controlcharts in real time and alerting operators and quality engineers to take samples andinitiate process improvements.in discrete units whichindicates the presenceor absence of somethingsuch as number of defects,injuries, errors, etc. Thisdata cannot have decimalsand cannot be used tocalculate other informationsuch as averages.Table of ContentsPart 1. Control Charts and Basic Considerations.Part 2. The Three Core Variables Charts: Using Sample Size to Determine Core Chart Type36Part 3. Special Processing Options . . . . . . . . . . . . . . . . . . . 10Sidebar - SPC for Very High Sampling Rates.InfinityQS International, Inc. 12601 Fair Lakes Circle Suite 250 Fairfax, VA 22033 www.infinityqs.com.2.19
A Practical Guide to Selecting the Right Control ChartPart 1. Control Charts and Basic ConsiderationsWhat IS and is NOT a Control Chart?Just to make sure we’re on the same page, let’s first clarify what a control chart is. Acontrol chart is a real-time, time-ordered, graphical process feedback tool designedto tell an operator when significant changes have occurred in the manufacturingprocess. Control charts tell the operator when to do something and when to donothing. A control chart illustrates process behaviors by detecting changes in a processoutput’s mean and/or standard deviation about the mean. Every processexhibits some normal levels of variation, but a control chart is designed toseparate this normal or “common cause” variation from special causeNote:It is important tovariations. Control charts indicate visually whether a process is innote that just becausecontrol (stable and predictable), or if it is out of control (unstable anda process is stable andunpredictable). Typically when the control chart indicates the processin-control doesn’t meanis out of control, an operator should take action to make adjustmentsits output is all withinto bring the process back under control or initiate an investigation intospecification limits.the root cause.Even though a control chart analysis is NOT the same as a capability analysis(a process’ ability to meet specifications), one should confirm that the process is in astate of statistical control before relying on the capability analysis results.Mean – The average ofA control chart is also NOT useful for receiving inspection because the samples arenot ordered in time of original production. Even though samples are taken, say 10parts out of 100 in a box, there is no time ordering of the sampling like there is on aproduction line, so a control chart is not relevant for this type of data. However, boxplots and histograms are perfectly suited for non-time-ordered data.a set of numbers suchControl charts should NOT be confused with run charts, which are time-ordered,but don’t have control limits. In addition, pre-control charts are not control chartsbecause these charts compare subgroup plot points with specification limits, notstatistical limits.by the number of samplesas sample data whichindicates the “central”value. It is calculated bytaking the sum of thesamples and then dividingtaken.Specification Limits– Requirements foracceptability of a processoutput typically set by theStandard Deviation –customer or engineering.An estimate of the variation from the mean for a larger population based on a givenTypically given as a number,sample. The formula for estimated standard deviation is:the target value, with upperY(x – x)2s n–1SSXXn estimated standard deviationsum ofindividual samplesample meansample sizeand lower limits whichdefine an acceptable range.The specification limit mayalso be given as a not toexceed number or a notless than number.InfinityQS International, Inc. 12601 Fair Lakes Circle Suite 250 Fairfax, VA 22033 www.infinityqs.com3
A Practical Guide to Selecting the Right Control ChartComponents of a Control ChartControl charts show time-ordered plotted points around a center line. The centerline is determined by calculating the mean of the plot points, typically about 20 to25 points. The upper (UCL) and lower control limits (LCL) are typically set at /- 3standard deviations of the plot points. The UCL and LCL show the expected normal(common cause) plot point variation. Control limits should be updated (recalculated)when the process improves. However, if you update the control limits when theprocess degrades, you are simply letting the process run with more variability.Updating the control limits only when the process improves promotes less variabilityand encourages continuous improvements over time.Note:Control limits are basedon observed process data,not on specification limits. Lineson a chart representing 75% of thespecification limit are not statisticalcontrol limits. Control limitsmay not always be centeredon target or within thespecification limits.Control charts are often divided into zones as shown.The 2 sigma and 1 sigma zones are sometimes used for early detectionof an unstable process. Certain patterns within these zones may alert anoperator to monitor more closely. For example, the operator may begin to seepatterns such as more plot points than usual in the 2 sigma zone causing him toincrease sampling or initiate an investigation.If the process is stable, 99.73% of the plot points should fall within the 3 sigma limitswith half of the points above the centerline and half below; 95% should fall within the2 sigma limits and 68% within the 1 sigma limits. Based on the normal distribution,control limits should be representative of 99.73% of a process’ “normal” state. Instatistical jabber, this means that when a plot point violates a control limit, there isonly a 0.27% chance (0.135% above UCL and 0.135% below LCL) that it was NOTa statistically significant event. Therefore, an out-of-control plot point is a rare eventwhen a process is behaving in a stable manner. Any points falling outside the controllimits should be treated as a special cause of variation and worthy of investigation.Normal Distribution –Variables data which hasa Gaussian (bell-shapedand symmetrical) curveor frequency distribution.Control charts are only validfor data which follows anormal distribution.InfinityQS International, Inc. 12601 Fair Lakes Circle Suite 250 Fairfax, VA 22033 www.infinityqs.com4
A Practical Guide to Selecting the Right Control ChartCalculating these limits and zones sounds complicated, but InfinityQS’ ProFicient software automatically computesthe mean, control limits, and standard deviation zones based on the sample data and chart selected. The softwaredisplays the sample data in real time as each new plot point is written to the ProFicient database.Basic Considerations for Selecting Control Chart TypeIn this guide we’ll take a look at three basic factors or questions to consider when determining the most appropriatecontrol chart for a given situation.1. What is the sample size?2. Do I need to group multiple process streams or part features on the same chart?3. Do I need to combine multiple “like features” that have different target values on the same chart?Your answers to each of these questions determine the most appropriate type of control chart to use for yoursituation. Simply use the decision tree shown here to guide your selection. Parts 2 through 3 in this guide providemore details for answering these questions, and the benefits and weaknesses of each type of control chart.Variable Data Control Chart Decision TreeInfinityQS International, Inc. 12601 Fair Lakes Circle Suite 250 Fairfax, VA 22033 www.infinityqs.com5
A Practical Guide to Selecting the Right Control ChartPart 2. The Three Core Variables Charts:Using Sample Size to Determine Core Chart TypeIn this section we’ll address question one, “ What is the sample size?”Question #1 What is the sample size?IX-MRXbar-RangeXbar-sYour answer to this question will lead you to a specific type of control chart as shownin the decision tree, with “n” being the sample size.Sample Size Equals One: Individual X – Moving Range (IX-MR)When your sample size is one (n 1), the chart to use is an Individual X – MovingRange chart (Individual X charts are also called X charts, I charts, IX charts, orindividuals charts).Examples of when to use a sample size of one include: Accounting data- daily overtime- number of parts scrapped for a given time periodHomogeneous batches (chemicals, liquid foods, etc.) where variationfrom consecutive samples would not indicate product variation, but onlymeasurement error Sampling is expensive and/or time consuming, or destructive testing(automotive crash-testing) Short production runs (e.g. five pieces in the entire run) Process automation sending only one rational data value (PLC sends one valueevery 5 minutes for an oven temperature)InfinityQS International, Inc. 12601 Fair Lakes Circle Suite 250 Fairfax, VA 22033 www.infinityqs.comIndividual X (IX) –The actual reading ormeasurement taken forquality control samplingpurposes.Moving Range – Theabsolute differencebetween two consecutiveindividual values (IX).6
A Practical Guide to Selecting the Right Control ChartThe IX-MR chart plots IX, the actual reading, and the Moving Range which is the absolute difference between twoconsecutive IX plot points. The chart below represents several batches of resin, a homogeneous mixture, and wewant to measure the percent solids of each batch. Highlighted in yellow (the 3rd plot point) in the ProFicient screenshot below, we see that the individual plot point on the IX chart is 5.0 and the Moving Range is 0.1. Notice thatfor subgroup 16, the moving range plot point exceeds the upper control limit of 0.9. This is an indication that thevariability in resin % solids exceeds what would be considered “normal.” That is, a special cause of variation ispresent in our process and there exists a need for investigation and possible process adjustment.Resin % SolidsTraditional IX-MR 1st Plot Point IX 5.2 MR 0 2nd Plot Point IX 4.9 MR 0.3/4.9-5.2/ 3rd Plot Point IX 5.0 MR 0.1/5.0-4.9/Note:Operators and othersfind these charts easy toread and understand, butfor sample sizes greater than9, they are not the mostaccurate indicators ofprocess variability.BenefitsWeaknesses Easy to Understand Only 15-25 measurements needed to estimatecontrol limitsDoes not independently separate variation in theaverage from variation in standard deviation Not sensitive enough to detect smallprocess changes Data can be plotted after each reading taken Minimum calculations neededInfinityQS International, Inc. 12601 Fair Lakes Circle Suite 250 Fairfax, VA 22033 www.infinityqs.com7
A Practical Guide to Selecting the Right Control ChartSample Size is Between Two and Nine (inclusively): Xbar – Range (Xbar-R)When your sample size is between 2 and 9 (2 n 9), then use the Xbar – Rangechart. Sample sizes between 2 and 9 (typically 3 or 5) are commonly used when atleast a few parts are made every hour and data are available to be collected at areasonable cost.The Xbar chart plots subgroup means, that is, the average of the individual valuesin the subgroup. The R chart plots the subgroup Range which is the differencebetween the maximum and the minimum individual values within the subgroup. In theexample chart above, the average of subgroup 8, is 2.7526 which is well within thecontrol limits. The range plot point is the difference between the highest and lowestvalues in the subgroup, 0.002, which is also well within the control limits. In fact, allplot points reside within the control limits indicating a consistent process where onlycommon cause variation is present.Range – The differencebetween the maximum andminimum individual values(IX) within a subgroup.Xbar Plot Point2.75232.7537 High2.7517 Low8.2577 3 2.7526Range Plot Point2.7537 - 2.7517 0.002Note:Operators and othersfind these charts easy toread and understand, butfor sample sizes greater than9, they are not the mostaccurate indicators ofprocess variability.BenefitsWeaknesses Separates variation in the averages from variationin the standard deviation Most widely recognized control chartMust use separate chart foreach characteristic on each part (the number ofcharts can add up quickly!) Principles used as the foundation for mostadvanced control charts No matter the sample size, only 2 individual valuesper subgroup are used to estimate the standarddeviation for the rangeInfinityQS International, Inc. 12601 Fair Lakes Circle Suite 250 Fairfax, VA 22033 www.infinityqs.com8
A Practical Guide to Selecting the Right Control ChartSample Size is Ten or Higher: Xbar – Standard Deviation (Xbar-s)When your sample size is 10 or higher (n 10), then use the Xbar – Standard Deviation chart. The Xbar-StandardDeviation chart is often referred to as either an Xbar-s or Xbar-SD chart. Using a sample size of ten or higher ismost common when lots of data are available and the costs for gathering the data is cheap. Examples include datafrom PLCs (Programmable Logic Controllers) or other automated data gathering devices. The Xbar-s chart is alsocommonly used for injection molding, multi-head filling operations, and continuous high speed production lineswhere it is possible to gather many measurements quickly and inexpensively.The Xbar-s chart plots the mean (the average of the individual values in the subgroup) and the sample standarddeviation of the individual values in the subgroup. In the chart below, subgroup 9 is highlighted. The average ofthe subgroup’s 10 plot points is 34.02 and shown on the top Xbar chart, while the standard deviation is 2.755 andplotted on the lower SD chart.BenefitsWeaknesses Very sensitive to small changes in the mean In most cases the standard deviation is a moreaccurate indicator of process variation thanthe rangeLarge amounts of data need to be gathered.Assuming 20 plot points and n 10, then 200values are needed to calculatecontrol limitsInfinityQS’ ProFicient software easily and quickly handles the data andcalculations for the Xbar-s chart all in real time. Don’t worry if the sample sizechanges with each subgroup, ProFicient can handle that too.InfinityQS International, Inc. 12601 Fair Lakes Circle Suite 250 Fairfax, VA 22033 www.infinityqs.comNote:If you arecurrently using themore popular Xbar-Rchart for sample sizes of 10or more, you will be betteroff using the Xbar-s chart tomore accurately indicateprocess changes.9
A Practical Guide to Selecting the Right Control ChartPart 3. Special Processing OptionsIn this section we’ll take a look at additional questions to ask related to grouping and combining data fromprocesses, parts, and test characteristics; Group Charts and Target Charts will also be introduced. If we look backat our original questions, we’ll be addressing questions 2 and 3 here.Group ChartsGroup charts address question 2 in our decision tree, “Do I need to group multiple data streams?” Group chartsare used to display several parameters, characteristics, or process streams on one chart in order to assess therelative uniformity or consistency among the multiple streams of data. Examples include: measuring shaft diameterin 3 places; cash register reconciliations among multiple registers; temperature measurements at various locationsin an oven; output from multiple fill heads.The power of a group chart is two-fold: one, to clearly and distinctly illustrate the extremes or lack of uniformity ina data set group; and two, to present the data to users so that opportunities for improvement are clearly detected.Question #2 Do I need to group multiple process streamsor part features on the same chart?InfinityQS International, Inc. 12601 Fair Lakes Circle Suite 250 Fairfax, VA 22033 www.infinityqs.com10
A Practical Guide to Selecting the Right Control Chart1.75411.7545High1.75391.75381.7544LowNote:The group chart isIn the example above, we want to see how uniform five journal bearingintentionally absent of controldiameters are from one crankshaft to the next and to each other. To chartlimits because sometimes groupthese diameters, we could create five separate charts, one for each charts are used for plotting dependentdiameter, but that’s a lot of charts and would make comparisons difficult.data streams. Pooling dependent dataInstead, we label each journal bearing diameter 1 through 5 and thenvalues typically results in incorrectcombine all readings on the same Group chart. A Group chart plotscontrol limits. Besides, Group chartsare more of a diagnostic andonly the minimum and maximum values from each group of diametersdiscovery tool than a traditionalwith the points labeled, identifying the diameter location. Of the 5 bearingprocess control tool.diameters in the illustration above, bearing 2 has the largest diameter at1.7545 while bearing 4 has the smallest at 1.7538. The results from thiscrankshaft are plotted as the first MAX and MIN point on the chart. Notice thatthe chart’s scale has been modified to only show the last two significant digits fromeach diameter (1.7545 45). Group charts are very sensitive and can easily detect differences among datastreams. In our example, bearing 2 is the maximum value three consecutivetimes. The chance of this happening randomly is only 0.8% (0.23 0.008). Veryquickly we see this may be worthy of investigation. MAX and MIN lines that track each other indicate the data streams are dependent. Converging lines suggest a decrease in within-part variation, i.e. closer lines more uniformity. In our example above, the fourth crankshaft is the most uniform.InfinityQS International, Inc. 12601 F
A Practical Guide to Selecting the Right Control Chart InfinityQS International, Inc. 12601 air Lakes Circle Suite 250 airfax, VA 22033 ww.infinityqs.com 7 The IX-MR chart plots IX, the actual reading, and the Moving Range which is the absolute difference between two
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