# NG BB 26 Control Charts

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- 1. UNCLASSIFIED / FOUO National GuardBlack Belt TrainingModule 26 Control ChartsUNCLASSIFIED / FOUO

2. UNCLASSIFIED / FOUOCPI Roadmap Measure 8-STEP PROCESS6. See 1.Validate2. Identify 3. Set 4. Determine5. Develop7. Confirm8. Standardize Counter-the Performance Improvement Root Counter-ResultsSuccessful MeasuresProblem GapsTargets Cause Measures& ProcessProcesses ThroughDefine Measure Analyze ImproveControl TOOLSProcess MappingACTIVITIES Map Current Process / Go & SeeProcess Cycle Efficiency/TOC Identify Key Input, Process, Output Metrics Littles Law Develop Operational Definitions Operational Definitions Develop Data Collection PlanData Collection Plan Validate Measurement System Statistical Sampling Collect Baseline Data Measurement System Analysis Identify Performance Gaps TPM Estimate Financial/Operational Benefits Generic Pull Determine Process Stability/CapabilitySetup Reduction Complete Measure Tollgate Control ChartsHistogramsConstraint IdentificationProcess Capability Note: Activities and tools vary by project. Lists provided here are not necessarily all-inclusive. UNCLASSIFIED / FOUO 3. UNCLASSIFIED / FOUO Learning Objectives Control chart fundamentals Use of control charts to identify Common Cause and Special Cause variation Factors to consider in constructing control charts Variables control charts Attribute control charts Understand the interpretation and application of these chartsUNCLASSIFIED / FOUO 3 4. UNCLASSIFIED / FOUO Control Chart Terms Control Chart = a time plot showing process performance, mean (average), and control limits The Voice of the Process !!! I-MR Chart of Pizza Preparation Time120 U C L=18.48 Individual Value15 _10 X=10.58 5 LC L=2.6736912 1518 21 24 2730Control charts measure the health of the processO bse r v ation10.0 U C L=9.717.5 Moving Range5.0 __ M R=2.972.50.0LC L=036912 1518 21 24 2730O bse r v ationUNCLASSIFIED / FOUO 5. UNCLASSIFIED / FOUO Control Chart Terms Control Limits = statistically calculated boundaries within which a process in control should operate These boundaries result from the process itself and areNOT customer specificationsI-MR Chart of Pizza Preparation Time120 U C L=18.48 Individual Value15 _10 X=10.58 5 LC L=2.67 36912 15 18 21 24 2730 O bse r v a tion10.0 U C L=9.717.5 Moving Range5.0 __ M R=2.972.50.0LC L=0 36912 15 18 21 24 2730 O bse r v a tionUNCLASSIFIED / FOUO5 6. UNCLASSIFIED / FOUO Common vs. Special Cause Measurements display variation Variation is either:Common Cause Variation This is the consistent, stable, random variability within the process We will have to make a fundamental improvement to reduce commoncause variation Is usually harder to reduceSpecial Cause Variation This is due to a specific cause that we can isolate Special cause variation can be detected by spotting outliers orpatterns in the data Usually easier to eliminate UNCLASSIFIED / FOUO 6 7. UNCLASSIFIED / FOUO Process Control When a process is in control This implies a stable, predictable amount of variation (commoncause variation) This does not mean a "good" or desirable amount of variation When a process is out-of-control This implies an unstable, unpredictable amount of variation It is subject to both common AND special causes of variation A process can be in statistical control and not capable of consistently producing good output within specification limits UNCLASSIFIED / FOUO 7 8. UNCLASSIFIED / FOUO Types of Control Charts The Control Chart family can be broken into two groups based on the type of data we are charting: Continuous/Variable Attribute/Discrete Since we prefer Continuous data we will study this group of Control Charts firstUNCLASSIFIED / FOUO 8 9. UNCLASSIFIED / FOUO Continuous Data Control Charts Thetheory of all Control Charts can be learned by studying the Xbar (Average) and R (Range) chart for continuous data We will then explore the I-MR (Individuals - Moving Range) Chart Xbar-R Charts allow us to study: Variation within each subgroup (precision) on the R chart Variation between each subgroup (accuracy) on the Xbar chart Note: Look at the R chart first, if it is in control, then look at the Xbar chart Examples of continuous data: width, diameter, temperature, weight, cycle times, etc. UNCLASSIFIED / FOUO 9 10. UNCLASSIFIED / FOUO Control Chart Assumptions Normally Distributed Data Control limits approximate +/- 3 sigma from the mean These control limits are based upon a normal distribution If the distribution of the data is non-normal, you must use one of thex-bar charts, because the x-bars are likely to be normally distributeddue to the effects of the Central Limit Theorem Rule of thumb for x-bar charts is subgroups of at least 4. Rarely isthe underlying distribution so far from normal to require largersubgroups to achieve normality in the x-bars. Independent Data Points Independence means the value of any given data point is notinfluenced by the value of any other data point (it is random) Violation of this assumption means the probability of any given datavalue occurring is not determined by its distance from the mean, butby its place in the sequence in a data series or patternUNCLASSIFIED / FOUO 10 11. UNCLASSIFIED / FOUOContinuous Data Control Charts Measurement (Continuous/Variable Data)Subgroup Size of 1Subgroup Size < 3-9 Subgroup Size > 9I-MRXbar-R Xbar-S UNCLASSIFIED / FOUO 11 12. UNCLASSIFIED / FOUO Continuous Data Control Charts Utilize probabilities and knowledge of the normal distribution I-MR chart is used: When you are learning about a process with few data points When sampling is very expensive When the sampling is by destructive testing and When you are building data to begin another chart type Xbar-R Chart is used with a sampling plan to monitor repetitiveprocesses. The sub-group sizes are from 3 to 9 items. Frequentlypractitioners will choose subgroups of 5. All of the theory of ControlCharts can be applied with these charts Xbar-SChart is used with larger sample groups of 10 or more items.Statisticians sometimes state that the standard deviation is only robustwhen the subgroup size is greater than 9 (These charts are similar tothe Xbar-R Chart)UNCLASSIFIED / FOUO 12 13. UNCLASSIFIED / FOUO Introduction to Xbar-R Xbar-R Charts are a way of displaying variable data Examples of variable data: width, diameter, temperature, weight,time, etc. RChart: a look at Precision Displays changes in the within subgroup dispersion of theprocess. Often called Short-Term Variation. Asks "Is the variation in the measurements within subgroupsconsistent? Must be in control before we can build or use the Xbar chart Xbar Chart: a look at Accuracy Shows changes in the average value of the process and is avisualization of the Longer-Term Variation Asks "Is the variation between the averages of the subgroupsmore than that predicted by the variation within the subgroups? UNCLASSIFIED / FOUO 13 14. UNCLASSIFIED / FOUO Mechanics of an Xbar-R Chart Control charts track processes by plotting data over time in the form:Range Chart X ChartUpper Control Limit Averages Upper Control LimitChart = X Double Bar + A2 R BarUpper Control Limit Range Chart = D4Rbar Upper Control LimitCenter Line Averages Chart =Average of the Subgroup Averages Center Line (X) Center Line Range Chart = Average of the Subgroup RangesCenter Line (R)Lower Control Limit AveragesChart = X Double Bar - A2 R BarLower Control Limit Lower Control Limit Range Chart = D3RbarUNCLASSIFIED / FOUO14 15. UNCLASSIFIED / FOUOExample: Xbar-R ChartStat > Control Charts > Variables Charts for Subgroups > Xbar-ROpen the worksheet data file called ORDER TAKING.MTWIn this file, orders are taken by order entry clerks. The data is the average holdtime a customer waits before speaking with a person to take their order.The delays are a problem, as many customers give up and we have a dropped calland lost orderUNCLASSIFIED / FOUO 15 16. UNCLASSIFIED / FOUOExample: Xbar-R ChartDouble click on C-1 Ave Hold TimeThis places it in the5 Variables boxType in 5 for your Subgroup sizeOur response is Ave. Hold Time and we choose 5 cells to represent our Subgroup sizeUNCLASSIFIED / FOUO 16 17. UNCLASSIFIED / FOUOHow Do We Interpret This Chart?Xbar-R Chart of Ave. Hold Time 1 16U C L=14.97 14Sample M eanXbar Chart 12 __X=10.88 108LC L=6.791 234 5 Sample 16U C L=15.01 12Sample Range R Chart8 _R=7.1040 LC L=01 234 5 Sample Always Look at the R Chart first ! Only if it is in control, is the Xbar chart usable ! UNCLASSIFIED / FOUO17 18. UNCLASSIFIED / FOUO Control Chart Data Requirements Data requirements for control chart applications:Must be in time series orderMinimum of 25 consecutive (no time gaps) subgroups orMinimum of 100 consecutive observationsUNCLASSIFIED / FOUO 18 19. UNCLASSIFIED / FOUO I-MR Chart The Individuals and Moving Range chart is also for continuous data It can be used for many transactional applications:Revenue or cost trackingCustomer satisfactionCall timesSystem response timesWait times Most common continuous measures time and money!UNCLASSIFIED / FOUO 19 20. UNCLASSIFIED / FOUO Individuals and Moving Range (I-MR) Chart I-MR Chart of Pizza Preparation Time1 20U C L=18.48Individual Value 15_ 10 X=10.585LC L=2.6736912 1518 21 24 27 30O bse r v ation 10.0 U C L=9.71 7.5Moving Range 5.0__M R=2.97 2.5 0.0LC L=036912 1518 21 24 27 30O bse r v ation The top chart is a plot of individual pizza preparation times The bottom chart is the Moving Range, in this case, the Range of two adjacent pizza preparation timesUNCLASSIFIED / FOUO 20 21. UNCLASSIFIED / FOUO Control Limit CalculationI Chart of Pizza Preparation Time 1 20UCL=18.48 UCL 15Individual Value_XX=10.58 10 5 LCLLCL=2.673 6912 1518 21 24 27 30 Observat ion The UCL (Upper Control Limit) and the LCL (Lower Control Limit) are calculated by Minitab using the sample/process data The control limits approximate +/- 3 standard devi