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- 1. UNCLASSIFIED / FOUO National Guard Black Belt Training Module 26 Control Charts UNCLASSIFIED / FOUO
- 2. UNCLASSIFIED / FOUOCPI Roadmap – Measure 8-STEP PROCESS 6. See 1.Validate 2. Identify 3. Set 4. Determine 5. Develop 7. Confirm 8. Standardize Counter- the Performance Improvement Root Counter- Results Successful Measures Problem Gaps Targets Cause Measures & Process Processes Through Define Measure Analyze Improve Control TOOLS •Process Mapping ACTIVITIES • Map Current Process / Go & See •Process Cycle Efficiency/TOC • Identify Key Input, Process, Output Metrics •Little’s Law • Develop Operational Definitions •Operational Definitions • Develop Data Collection Plan •Data 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/Capability •Setup Reduction • Complete Measure Tollgate •Control Charts •Histograms •Constraint Identification •Process 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 charts UNCLASSIFIED / 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 Time 1 20 U C L=18.48 Individual Value 15 _ 10 X=10.58 5 LC L=2.67 3 6 9 12 15 18 21 24 27 30 Control charts measure the “health” of the process O bse r v ation 10.0 U C L=9.71 7.5 Moving Range 5.0 __ M R=2.97 2.5 0.0 LC L=0 3 6 9 12 15 18 21 24 27 30 O bse r v ation UNCLASSIFIED / 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 are NOT customer specifications I-MR Chart of Pizza Preparation Time 1 20 U C L=18.48 Individual Value 15 _ 10 X=10.58 5 LC L=2.67 3 6 9 12 15 18 21 24 27 30 O bse r v a tion 10.0 U C L=9.71 7.5 Moving Range 5.0 __ M R=2.97 2.5 0.0 LC L=0 3 6 9 12 15 18 21 24 27 30 O bse r v a tion UNCLASSIFIED / FOUO 5
- 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 common cause variation Is usually harder to reduce Special Cause Variation This is due to a specific cause that we can isolate Special cause variation can be detected by spotting outliers or patterns 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 (common cause 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 first UNCLASSIFIED / FOUO 8
- 9. UNCLASSIFIED / FOUO Continuous Data Control Charts The theory 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 the x-bar charts, because the x-bars are likely to be normally distributed due to the effects of the Central Limit Theorem Rule of thumb for x-bar charts is subgroups of at least 4. Rarely is the underlying distribution so far from normal to require larger subgroups to achieve normality in the x-bars. Independent Data Points “Independence” means the value of any given data point is not influenced by the value of any other data point (it is random) Violation of this assumption means the probability of any given data value occurring is not determined by its distance from the mean, but by its place in the sequence in a data series or pattern UNCLASSIFIED / FOUO 10
- 11. UNCLASSIFIED / FOUOContinuous Data Control Charts Measurement (Continuous/Variable Data) Subgroup Size of 1 Subgroup Size < 3-9 Subgroup Size > 9 I-MR Xbar-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 repetitive processes. The sub-group sizes are from 3 to 9 items. Frequently practitioners will choose subgroups of 5. All of the theory of Control Charts can be applied with these charts Xbar-S Chart is used with larger sample groups of 10 or more items. Statisticians sometimes state that the standard deviation is only robust when the subgroup size is greater than 9 (These charts are similar to the 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. R Chart: a look at “Precision” Displays changes in the „within‟ subgroup dispersion of the process. Often called “Short-Term Variation.” Asks "Is the variation in the measurements „within‟ subgroups consistent?” 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 a visualization of the “Longer-Term Variation” Asks "Is the variation „between‟ the averages of the subgroups more 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 Chart Upper Control Limit Averages Upper Control Limit Chart = X Double Bar + A2 R Bar Upper Control Limit Range Chart = D4Rbar Upper Control Limit Center Line Averages Chart = Average of the Subgroup Averages Center Line (X) Center Line Range Chart = Average of the Subgroup Ranges Center Line (R) Lower Control Limit Averages Chart = X Double Bar - A2 R Bar Lower Control Limit Lower Control Limit Range Chart = D3Rbar UNCLASSIFIED / FOUO 14
- 15. UNCLASSIFIED / FOUOExample: Xbar-R Chart Stat > Control Charts > Variables Charts for Subgroups > Xbar-R Open the worksheet data file called ORDER TAKING.MTW In this file, orders are taken by order entry clerks. The data is the average hold time 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 call and lost order UNCLASSIFIED / FOUO 15
- 16. UNCLASSIFIED / FOUOExample: Xbar-R Chart Double click on C-1 Ave Hold Time This places it in the 5 Variables box Type in 5 for your Subgroup size Our response is Ave. Hold Time and we choose 5 cells to represent our Subgroup size UNCLASSIFIED / FOUO 16
- 17. UNCLASSIFIED / FOUOHow Do We Interpret This Chart? Xbar-R Chart of Ave. Hold Time 1 16 U C L=14.97 14 Sample M eanXbar Chart 12 _ _ X=10.88 10 8 LC L=6.79 1 2 3 4 5 Sample 16 U C L=15.01 12 Sample Range R Chart 8 _ R=7.10 4 0 LC L=0 1 2 3 4 5 Sample Always Look at the R Chart first ! Only if it is in control, is the Xbar chart usable ! UNCLASSIFIED / FOUO 17
- 18. UNCLASSIFIED / FOUO Control Chart Data Requirements Data requirements for control chart applications: Must be in time series order Minimum of 25 consecutive (no time gaps) subgroups or Minimum of 100 consecutive observations UNCLASSIFIED / 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 tracking Customer satisfaction Call times System response times Wait 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 Time 1 20 U C L=18.48 Individual Value 15 _ 10 X=10.58 5 LC L=2.67 3 6 9 12 15 18 21 24 27 30 O bse r v ation 10.0 U C L=9.71 7.5 Moving Range 5.0 __ M R=2.97 2.5 0.0 LC L=0 3 6 9 12 15 18 21 24 27 30 O 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 times UNCLASSIFIED / FOUO 20
- 21. UNCLASSIFIED / FOUO Control Limit Calculation I Chart of Pizza Preparation Time 1 20 UCL=18.48 UCL 15 Individual Value _ X X=10.58 10 5 LCL LCL=2.67 3 6 9 12 15 18 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 deviations (99+% of the data) Here, 99+% of the pizzas are prepared between 2.6 and 18.7 minutes Be careful not to confuse control limits and specification limits! If a data point appears outside of the control limits, there is less than a 1% chance that this was part of the normal process. Since it is very unlikely that this value occurred by chance, it is called “Special Cause” variation. UNCLASSIFIED / FOUO 21
- 22. UNCLASSIFIED / FOUO Control Limit Interpretation I Chart of Pizza Prep Time 2 1 20.0 17.5 1 15.0 UCL=15.29 Individual Value 12.5 _ 10.0 X=9.87 7.5 3 3 3 3 3 3 3 3 5.0 3 LCL=4.45 3 6 9 12 15 18 21 24 27 Observation Another type of Special Cause variation occurs when there is a predictable pattern in the data The predictable pattern of the data means the data is not random and that there is an underlying reason for this pattern – a Special Cause The Western Electric rules are helpful in identifying patterns in the data (these are in the appendix) UNCLASSIFIED / FOUO 22
- 23. UNCLASSIFIED / FOUO Exercise: Begin Building an I-MR Chart Let‟s begin building an I-MR chart for a Pizza Preparation process. Begin by using the 5 Pizza Preparation Time measurements below to start the calculations for a Control Chart on a flip-chart. Individuals Chart Plot each individual time measurement Calculate the Centerline The centerline on an Individuals chart is the overall average Verify that the average is 9.6 The control limits will be calculated by a formula in Minitab. They approximate +/- 3 standard deviations of the pizza prep times UNCLASSIFIED / FOUO 23
- 24. UNCLASSIFIED / FOUO Pizza Exercise Moving Range Chart Calculate the ranges The first range is between points 1 and 2 Range = Max - Min 12 - 7 = 5 The next range is between points 2 and 3 Range = Max - Min 11 - 7 = 4 Continue for the next 2 ranges UNCLASSIFIED / FOUO 24
- 25. UNCLASSIFIED / FOUO Pizza Exercise (Cont.) Moving Range Chart Calculate the Centerline The centerline is the average of the moving ranges, called R For these 5 points (4 range calculations), verify that R = 3 The Control Limits will be calculated in Minitab. In this case they approximate +/- 3 standard deviations of the range values. We expect the Control Limits to be tighter for the Moving Range chart than for the Individuals chart UNCLASSIFIED / FOUO 25
- 26. UNCLASSIFIED / FOUOBuild I-MR Chart in Minitab Let‟s continue with our exercise: 1. Open the exercise Exercise9.mtw 2. Choose: Stat> Control Charts> Variables Charts for Individuals> I-MR UNCLASSIFIED / FOUO 26
- 27. UNCLASSIFIED / FOUOI-MR Input Window 3. Double click on C1 Pizza Preparation Time. This places it in the Variables box. 4. Click OK UNCLASSIFIED / FOUO 27
- 28. UNCLASSIFIED / FOUO Individual and Moving Range (I-MR) Chart I-MR Chart of Pizza Preparation Time 1 20 U C L=18.48 Individual Value 15 _ 10 X=10.58 5 LC L=2.67 3 6 9 12 15 18 21 24 27 30 O bser vation 10.0 U C L=9.71 7.5 M oving Range 5.0 __ M R=2.97 2.5 0.0 LC L=0 3 6 9 12 15 18 21 24 27 30 O bser vation Is our Pizza Prep process in statistical control? Is the process likely to be acceptable to our customers? UNCLASSIFIED / FOUO 28
- 29. UNCLASSIFIED / FOUOWestern Electric Rules Remember the tests that we used in Run Charts? These are used in Control Charts as well. The additional tests are called the “Western Electric Rules” They can be found under Stat>Control Charts>Variables Charts for Individuals>I-MR>I-MR Options>Tests UNCLASSIFIED / FOUO 29
- 30. UNCLASSIFIED / FOUO Control Chart Tests Upper Control Limit Point outside of the limit: Control limits are calculated to measure the Center Line natural variability of a process. Any point on, or outside, the limit is considered Lower Control Limit abnormal and requires investigation. Run: Upper Control Limit A “run” is a series of points occurring Center Line continually on one side of the center line. A “run” of seven points is considered abnormal. Lower Control Limit Also considered abnormal: 10 out of 11,12 of 14, or 16 of 20 points on one side of the center line. Upper Control Limit Trending: Center Line Seven points in a continuous upward or downward direction. Lower Control Limit UNCLASSIFIED / FOUO
- 31. UNCLASSIFIED / FOUOControl Chart Tests Upper Control Limit Approaching the center line (hugging): When most points lie within the center line and 1.5s it is not a controlled state and usually means CL the mixing of data from different populations. This Lower Control Limit makes the control limits too wide and stratification of data is usually necessary. Upper Control Limit Cycling (periodicity): CL Any repeated up and down trend is abnormal and requires investigation. Lower Control Limit UCL Approaching control limits: CL 2 of 3 points lying outside the 2s line is considered abnormal. LCL UNCLASSIFIED / FOUO
- 32. UNCLASSIFIED / FOUO Special Causes Are Clues to the Process A control chart is a guide to improving your process Take advantage of every clue Identify and investigate all special causes – they teach us how things affect the process Some special causes are good! For example, in our pizza delivery case, a delivery time out of control on the low side would be good. We could investigate this case to try to discover a new best practice. UNCLASSIFIED / FOUO 32
- 33. UNCLASSIFIED / FOUO Process for Identifying Special Causes Check all the W.E. rules each time you plot a point Look across the entire chart Circle all special causes Investigate immediately – this is especially important. Do not lose the opportunity to learn as much as possible about the conditions that caused this special cause variability. Take notes on the investigation You must investigate and eliminate the special cause! UNCLASSIFIED / FOUO 33
- 34. UNCLASSIFIED / FOUO Next Steps Identify assignable causes Establish that the data are normally distributed without the special cause data points Circle the special causes Eliminate special causes from the control limit calculation Recalculate control limits UNCLASSIFIED / FOUO 34
- 35. UNCLASSIFIED / FOUONew Control Limits I-MR Chart of Pizza Preparation Time 1 1 20 U C L=18.86 If you can investigate Indiv idual V alue 15 and determine what 10 _ X=10.69 caused these 5 „Out of Control‟ LC L=2.52 points, you can then 0 3 6 9 12 15 18 21 24 27 30 delete them and Observation recalculate your 10.0 1 U C L=10.04 control chart limits M ov ing Range 7.5 5.0 __ MR=3.07 2.5 0.0 LC L=0 3 6 9 12 15 18 21 24 27 30 Observation UNCLASSIFIED / FOUO 35
- 36. UNCLASSIFIED / FOUO Attribute Control Charts UNCLASSIFIED / FOUO
- 37. UNCLASSIFIED / FOUO Attribute Data Charts Two categories of attribute data: Count data (outcomes: 0, 1, 2, 3, 4, 5, etc.) Good/bad product data (only 2 possible outcomes) Four common attribute charts: C and U charts are used for count data of Errors in the process, either a step in the process or the overall process, or Defects in the process‟ or steps‟ deliverables NP and P charts are used for good/bad process, service, or product data (items or process steps that are defective or flawed) UNCLASSIFIED / FOUO 37
- 38. UNCLASSIFIED / FOUO Which Chart to Use? Count or Classification (Discrete/Attribute Data) Defects Defective Units Fixed Variable Fixed Variable sample sizes sample sizes sample sizes sample sizes C Chart U Chart, NP Chart, P Chart, “defect count“ “defects / unit” “no. defective” “proportion ” Discrete/Attribute Data To select an attribute chart, first choose between plotting defects or defective units. Then decide between fixed or variable opportunity. The variable opportunity charts are used more frequently. UNCLASSIFIED / FOUO 38
- 39. UNCLASSIFIED / FOUO Deeper into Attribute Charts Many transactional processes and manufacturing processes only record data as to the service or the products being either bad or good, defective or not defective There are two sub-families in the Attribute control charts: If we count defects (usually with any item having more than one opportunity for a defect) we use the C or Ucharts If the sample size is always the same, use a C-chart. If the sample size varies, use a U-chart. If we count defective units instead of defects, we use the NP or P charts If the sample size is always the same, use a NP-chart. If the sample size varies, use a P-chart. UNCLASSIFIED / FOUO 39
- 40. UNCLASSIFIED / FOUO Charts for Attribute Data Most of the Attribute Control Charts are identical in interpretation and very similar to create in Minitab The equations used are slightly different, but still based on the theory we learned with the Xbar Chart One of the most commonly used attribute charts is the P-Chart which plots Proportion Defective If you calculated Proportion Defective as your baseline capability metric – this chart is for you! UNCLASSIFIED / FOUO 40
- 41. UNCLASSIFIED / FOUO P-Chart P-Charts should be used whenever we are monitoring proportion defective (percentage defective is just another proportion) Some uses of the P-Chart in transactional applications would be: Billing errors (proportion of total bills that had errors) Defective loan applications Proportion of invoices with errors Proportion of missing reservations Defective room service orders Missing items Proportion of customers who were dissatisfied with service UNCLASSIFIED / FOUO 41
- 42. UNCLASSIFIED / FOUO P-Chart Pizza Exercise Anthonys Pizza wishes to monitor defective pizzas Each day for a month the cook keeps a count of the number of defective pizzas for that day and also the total number of pizzas that day Let‟s use the first 5 days data below to start the P- Chart on a flipchart UNCLASSIFIED / FOUO 42
- 43. UNCLASSIFIED / FOUO P-Chart Pizza Exercise (Cont.) Calculate the proportion defective Recall the formula for proportion defective: Number of Defective Units Proportion Defective Total Units In this example: Number of Defective Pizzas Proportion Defective Total Pizzas For the first day: 9 Proportion Defective 0.021 420 Note: Percentage Defective, in this case, would be 2.1% defective Calculate the proportion defective for days 2-5 UNCLASSIFIED / FOUO 43
- 44. UNCLASSIFIED / FOUO P-Chart Pizza Exercise (Cont.) Next, calculate the center line The center line is the proportion of Total Defectives (for all samples) to Total Units (for all samples) Verify that this is 0.019 The Control Limits are calculated in Minitab The equations are slightly different, but the Control Limits are still calculated from the actual values, predicting the range of 99% of the data UNCLASSIFIED / FOUO 44
- 45. UNCLASSIFIED / FOUO Minitab - Attributes Control Charts 1. Open worksheet: Exercise9.mtw 2. Choose Stat>Control Charts>Attributes Charts>P UNCLASSIFIED / FOUO 45
- 46. UNCLASSIFIED / FOUOP-Chart Input Window 3. Double click on C-4 Defective Pizzas. This places it in the Variables box. 4. Place cursor in the Subgroups sizes box and then double click on C-5 Number of Pizzas to move it there 5. Click OK Note: Minitab calculates the proportion defective for us. We enter the defective units in the Variable box. Then we enter the total units over that time period in the Subgroup sizes box. UNCLASSIFIED / FOUO 46
- 47. UNCLASSIFIED / FOUO P-Chart P Chart of Defective Pizzas 0.05 1 Note: Minitab recalculates 0.04 the control limits every UCL=0.03689 time the subgroup size 0.03 changes. Proportion To get a straight line, you _ 0.02 P=0.01932 can enter a constant value under “Subgroup size.” 0.01 In this example, the best LCL=0.00174 constant would be the 0.00 average of the “Number of 3 6 9 12 15 18 21 24 27 30 Sample Pizzas.” Tests performed with unequal sample sizes What are your thoughts around our defective pizzas? UNCLASSIFIED / FOUO 47
- 48. UNCLASSIFIED / FOUO Exercise: Create a Control Chart Now Anthonys Pizza wants to investigate sales history and billing errors for the same month In teams, continue with Exercise9.mtw. Use an I- MR Chart to monitor sales for the month. Use a P-Chart to observe the proportion of defective bills Prepare to teach back to the class on your findings UNCLASSIFIED / FOUO 48
- 49. UNCLASSIFIED / FOUO Quick Review - Control Chart Reminders There are several types of control charts: Determine type of data: continuous or attribute Be clear on the purpose and value you wish to gain from the chart Control limits are derived from process data UNCLASSIFIED / FOUO 49
- 50. UNCLASSIFIED / FOUO Control Chart Uses and Benefits Demonstrate stability and predictability of a process over time Range of variation within the “control limits” Distinguish between common vs. special cause variation Provides more information than Run Charts Can be used to demonstrate changes in performance Provide a common language for process performance Offer early warning of problems BUT….. UNCLASSIFIED / FOUO 50
- 51. UNCLASSIFIED / FOUO Control Chart Challenges Must use correct type of chart for the data Must meet normality and independence assumptions Non-normal, continuous data must use x-bar chart to meet normality requirement Control limits vs. customer requirements Remember that the control limits are providing the Voice of the Process We need to look at specification limits to see the Voice of the Customer A process “in control” may be ineffective, inefficient, or both! Control charts require effective, ongoing data collection. To be effective for determining root causes of special cause variation, they must be reacted to immediately! UNCLASSIFIED / FOUO 51
- 52. UNCLASSIFIED / FOUO Steps in Control Charting Select process characteristic to control, the key x or Y Collect data and calculate appropriate statistics Assess data distribution normality Construct preliminary control charts Establish control (find and eliminate special causes) Construct final control charts Establish stability (find and reduce common causes) Use for ongoing control purposes UNCLASSIFIED / FOUO 52
- 53. UNCLASSIFIED / FOUO What Do Control Charts Tell Us? When the process mean has shifted I-MR Chart of Pizza Preparation Time 1 1 20 U C L=18.86 When process variability has changed Individual V alue 15 _ 10 X=10.69 When special causes are present 5 LC L=2.52 0 3 6 9 12 15 18 21 24 27 30 Process is not predictable O bser vation 1 10.0 U C L=10.04 Opportunity to learn about the process M oving Range 7.5 5.0 When no special causes are present __ M R=3.07 2.5 0.0 LC L=0 Process is predictable 3 6 9 12 15 18 21 24 27 30 O bser vation No clues to improvement available; may need to introduce a special cause in order to understand cause and effect, and then to effect a change Control charts tell you when, not why!! UNCLASSIFIED / FOUO 53
- 54. UNCLASSIFIED / FOUO Process Control Chart Template I-MR Chart of Delivery Time The current baseline 40 delivery time is stable UC L=37.70 over time with both Indiv idual V alue 35 the Moving Range 30 _ X=29.13 (3.22 days) and 25 Individual Average LC L=20.56 (29.13 days) 20 1 28 55 82 109 136 163 190 217 244 experiencing common Observation cause variation 10.0 UC L=10.53 255 data points M ov ing Range 7.5 collected with zero 5.0 subgroups, thus the __ MR=3.22 2.5 I&MR control chart 0.0 LC L=0 selected 1 28 55 82 109 136 163 190 217 244 Observation - Example - Required As Applicable UNCLASSIFIED / FOUO
- 55. UNCLASSIFIED / FOUO Exercise: Prepare a Control Chart Objective Create control charts for the GGAs Budget Department Instructions Identify Primary Y metric Determine best control charts to use Run proper control chart for that data Time = 15 Minutes UNCLASSIFIED / FOUO 55
- 56. UNCLASSIFIED / FOUO Takeaways Control limits are calculated from a time series of the characteristic we are measuring Different formulas are available, depending on the type of data Control limits should not be recalculated each time data are collected The control limits are a function of the sampling and subgrouping plan Variation due to "assignable cause" is often the easiest variation to reduce/eliminate Control limits are not related to standards! Nor are they specifications! Control limits are a measure of what the process is doing/has done. It is the present/past tense, not the future (what we want the process to do or what it has the potential to do) UNCLASSIFIED / FOUO 56
- 57. UNCLASSIFIED / FOUO What other comments or questions do you have? UNCLASSIFIED / FOUO
- 58. UNCLASSIFIED / FOUO References Wheeler, Donald J. & Chambers, David S., Understanding Statistical Process Control, Second Edition, SPC Press, Knoxville Tennessee, 1992 Pruit, James M. & Snyder, Helmut, Essentials of SPC in the Process Industries, Instrument Society of America, 1996 UNCLASSIFIED / FOUO 58
- 59. UNCLASSIFIED / FOUO APPENDIX UNCLASSIFIED / FOUO
- 60. UNCLASSIFIED / FOUO Western Electric Rules 1. One point beyond Zone A Detects a shift in the mean, an increase in the standard deviation, or a single aberration in the process. For interpreting Test 1, the R chart can be used to rule out increases in variation. 2. Nine points in a row in Zone C or beyond Detects a shift in the process mean 3. Six points in a row steadily increasing or decreasing Detects a trend or drift in the process mean. Small trends will be signaled by this test before Test 1. UNCLASSIFIED / FOUO 60
- 61. UNCLASSIFIED / FOUO Western Electric Rules (Cont.) 4. Fourteen points in a row alternating up and down Detects systematic effects, such as two alternately used machines, vendors, or operators 5. Two out of three points in a row in Zone A or beyond Detects a shift in the process average or increase in the standard deviation. Any two out of three points provide a positive test. 6. Four out of five points in Zone B or beyond Detects a shift in the process mean. Any four out of five points provide a positive test. UNCLASSIFIED / FOUO 61
- 62. UNCLASSIFIED / FOUO Western Electric Rules (Cont.) 7. Fifteen points in a row in Zone C, above and below the center line Detects stratification of subgroups when the observations in a single subgroup come from various sources with different means 8. Eight points in a row on both sides of the center line with none in Zone C Detects stratification of subgroups when the observations in one subgroup come from a single source, but subgroups come from different sources with different means UNCLASSIFIED / FOUO 62

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