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UNCLASSIFIED / FOUO UNCLASSIFIED / FOUO National Guard Black Belt Training Module 27 Process Capability UNCLASSIFIED / FOUO UNCLASSIFIED / FOUO
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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 2
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UNCLASSIFIED / FOUO Learning Objectives Learn prerequisites for conducting process capability studies Learn how Cp and Cpk are calculated and how to interpret the Minitab output Learn how to handle continuous and attribute data UNCLASSIFIED / FOUO 3
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UNCLASSIFIED / FOUO Process Capability – What Is It? Most measures have some target value and acceptable limits of variation around the target – usually set by the customer The extent to which the “expected” values fall within these customer specification limits determines how capable the process is of meeting its requirements Consider key measures of process performance in: Help Desk Responsiveness Job Acceptance Rate Customer Queue Time Service Treatment (complaints) Service Cost / Order On-Time Delivery Process Capability UNCLASSIFIED / FOUO 4
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UNCLASSIFIED / FOUO Process Capability – Cp Ratio of total variation allowed by the specification to the total variation actually measured from the process Use Cp when the mean can easily be adjusted (i.e., transactional processes where resources can easily be added with no or minor impact on quality) AND the mean is monitored (so process owner will know when adjustment is necessary – doing control charting is one way of monitoring) Typical goals for Cp are greater than 1.33 (or 1.67 for safety items) If Cp < 1, then the variability of the process is greater than the specification limits Process Capability UNCLASSIFIED / FOUO 5
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UNCLASSIFIED / FOUO Process Capability – Cp Allowed variation (spec.) (USL - LSL) Cp or Cp Normal variation of the process 6 99.7% of values -3 +3 Process Width LSL T USL Process Capability UNCLASSIFIED / FOUO 6
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UNCLASSIFIED / FOUO A Metaphor for Cp – Parking Vehicles 1 Cp measures the width of the vehicle in the street and compares it to the width of the parking place without parking the vehicle. Cp < 1 Cp ≈ 1 Cp >> 1 Process Capability UNCLASSIFIED / FOUO 7
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UNCLASSIFIED / FOUO Process Capability – Cpk This index accounts for the dynamic mean shift in the process – the amount that the process is off target USL x x LSL C pk Min or 3σ 3σ Calculate both values and report the smaller number Process Capability UNCLASSIFIED / FOUO 8
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UNCLASSIFIED / FOUOProcess Capability – Cpk, CPU, CPL Most common calculation of Process Capability Ratio of the range between the sample mean and the nearest specification to 3 standard deviations. Use when the mean cannot be easily adjusted (i.e., Cycle times, customer satisfaction indices, etc.) Typical goals for Cpk are greater than 1.33 (or 1.67 if safety related) For Cpk Std. Deviation estimates use: Rbar/d2 [short term] (calculated from Xbar-R chart) Process Capability UNCLASSIFIED / FOUO 9
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UNCLASSIFIED / FOUO A Metaphor for Cp – Parking Vehicles 1 +/- 3 σ (Voice of Process) Cp ≈ 1.3 +/- 3 σ (Voice of Process) Voice of Customer +/- 3 σ (Voice of Process) For Cp, it doesn‟t matter where the process is relative to the specifications, only the width of the process to the width of the specifications. Process Capability UNCLASSIFIED / FOUO 10
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UNCLASSIFIED / FOUO A Metaphor for Cpk – Parking Vehicles 2 Cpk ≈ 1.3 +/- 3 σ (Voice of Process) Cpk ≈ 1.3 : the process has room to move before exceeding a customer specification. In other words, at least the driver and/or the passenger can get out of the HMMWV . Process Capability UNCLASSIFIED / FOUO 11
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UNCLASSIFIED / FOUO A Metaphor for Cpk – Parking Vehicles 2 +/- 3 σ (Voice of Process) Cpk ≈ 0 Specifications (Voice of Customer) Cpk ≈ 0: The center of the process is on (or equal to) a customer specification (either side)! Process Capability UNCLASSIFIED / FOUO 12
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UNCLASSIFIED / FOUO A Metaphor for Cpk – Parking Vehicles 2 Specifications (Voice of Customer) Cpk ≈ -1 +/- 3 σ (Voice of Process) Cpk ≈ -1: The center of the process is outside the customer specifications (either side)! Process Capability UNCLASSIFIED / FOUO 13
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UNCLASSIFIED / FOUO Uses of Capability Analysis Performed on existing processes as a means of establishing a baseline of current operations (so it‟s possible to tell when improvement has occurred) When done periodically, is a means of monitoring change (good or bad) of a process for whatever reason (system, personnel, environment, etc.) Can be done on any process that has a target spec. established (target spec. is needed for the values in numerator), and has a capable measuring system (needed for valid values in denominator) Process Capability UNCLASSIFIED / FOUO 14
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UNCLASSIFIED / FOUO Process Capability – CPU CPU indicates capability against an Upper Specification Limit. In the next example, the average delivery time of a Pizza Company is within the 30 minute requirement. However, the histogram shows that quite a few deliveries are exceeding the 30 minute upper spec. limit The CPU figure of 0.139 confirms that the process is incapable (<1) Process Capability UNCLASSIFIED / FOUO 15
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UNCLASSIFIED / FOUO Process Capability – CPU USL- X Cpu= 3s Process Capability UNCLASSIFIED / FOUO 16
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UNCLASSIFIED / FOUO Minitab Exercise Open Minitab file: Exercise 235.mtw Click Stat>Quality Tools>Capability Sixpack>Normal Note: This exercise is based on a different dataset than previous slides so different, unrelated results can be expected. Process Capability UNCLASSIFIED / FOUO 17
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UNCLASSIFIED / FOUOMinitab Exercise (Cont.) 1. Double click on C-5 Delivery Time to Place it in the box for Single column 2. In the Subgroup size Box, type a 1 since our Sample size is one 3. For Upper Spec type in 30 minutes (given) 4. Click on OK Note: For Process Capability you must have at least 1 Spec Limit Process Capability UNCLASSIFIED / FOUO 18
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UNCLASSIFIED / FOUO Minitab Exercise (Cont.) Process Capability Sixpack of Delivery Time I Chart Capability Histogram 40 USL UCL=37.71 On both the I ChartS L 30 S pecifications Individual Value U 30 _ X=29.12 and the Moving Range Chart, the points are 20 1 28 55 82 109 136 163 190 217 244 LCL=20.53 randomly distributed 24 26 28 30 32 34 36 Moving Range Chart between the control Normal Prob Plot 10 UCL=10.55 limits, D: 1.947, P : < 0.005 Aimplying a stable process . Moving Range 5 __ MR=3.23 0 LCL=0 1 28 55 82 109 136 163 190 217 244 20 25 30 35 Last 25 Observations 35 The points Capability Plot O v erall Within on Within Last 25 the Observations chart make a S tDev 2.86364 S tDev 2.68251 Values 30 random scatter, with pno * Cp C pk * 0.1 O v erall P P pk 0.11 25 trends or shifts, which also S pecs C pm * 245 250 255 Observation 260 265 indicates process stability. Process Capability UNCLASSIFIED / FOUO 19
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UNCLASSIFIED / FOUO Minitab Exercise (Cont.) Process Capability Sixpack of Delivery Time I Chart Capability Histogram The data in the Capability Histogram 40 USL UCL=37.71 approximately follow the normal curve. On the S pecifications Individual Value U S L 30 normal 30probability plot, the points extend _X=29.12 outside the 95% confidence interval and have a p-value < 0.05, which indicates that our LCL=20.53 20 data is non-normal82. 109 136 163 190 217 244 1 28 55 24 26 28 30 32 34 36 Moving Range Chart Normal Prob Plot Since the data is non-normal, we have UCL=10.55 A D: 1.947, P : < 0.005 10 consulted our MBB who conducted a more Moving Range thorough analysis that indicated we are still 5 __ OK using a normal probability analysis. MR=3.23 0 LCL=0 1 28 55 82 109 136 163 190 217 244 20 25 30 35 Last 25 Observations Capability Plot 35 Within Within O v erall S tDev 2.86364 S tDev 2.68251 Values Cpk is 0.1 30 Cp * Pp * O v erall C pk 0.1 P pk 0.11 25 Is our process capable? S pecs C pm * 245 250 255 260 265 Observation Process Capability UNCLASSIFIED / FOUO 20
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UNCLASSIFIED / FOUO Process Capability – CPL CPL indicates capability against a Lower Specification Limit Army Lodging has been getting complaints about its slow elevators and decided to collect data to investigate. In this example, the speed of an elevator computer is unacceptable below 150 cm/sec. The CPL of 1.48 indicates the process is “capable” of meeting the specifications if it continues within the same range of variation Process Capability UNCLASSIFIED / FOUO 21
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UNCLASSIFIED / FOUO Process Capability – CPL (Cont.) Cpl= X - LSL 3s _ Process Capability UNCLASSIFIED / FOUO 22
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UNCLASSIFIED / FOUO Process Capability – Cpk Cpk is the index used when a process has a “two-sided” specification Army Lodging is concerned that the temperatures of its guest rooms may vary too widely. In this example, the temperature of a guest room needs to be between 62 and 70 degrees Fahrenheit for the guest to be comfortable. We determine Cpk by calculating both CPU and CPL Cpk is the smaller of the two! You can see that while almost no rooms are too cold, some rooms are too hot – which is reflected in the Cpk of 0.36 (which is much less than 1) Process Capability UNCLASSIFIED / FOUO 23
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UNCLASSIFIED / FOUO Process Capability – Cpk (Cont.) Cpk = Cpl or Cpu (whichever is smaller) _ _ , Process Capability UNCLASSIFIED / FOUO 24
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UNCLASSIFIED / FOUO Process Capability – Cpk _ _ USL x x LSL Cpk Min or 3s 3s Calculate both values and report the smaller number. Process Capability UNCLASSIFIED / FOUO 25
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UNCLASSIFIED / FOUO Capability Action Plan Give highest priority to parameters with Cpk‟s less than 1.0 (center the dimension, reduce the variation or both) If possible, get tolerance relief. (If product/process is mature, and there have been no customer problems, what is the need for this formal spec when another “de facto” spec has been used historically?) 100% inspect, measure and sort Chart using the data from the measurements Use SPC Charting on parameters with Cpk‟s between 1.0 and 1.33 (or 1.67 if safety related) Process Capability UNCLASSIFIED / FOUO 26
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UNCLASSIFIED / FOUO What About Attribute Data? Use Capability Analysis (Binomial) to produce a process capability report when your data are from a binomial distribution Binomial distributions are usually associated with recording the number of defective items out of the total number sampled Examples: You might have a pass/fail measurement that determines whether a service met expectations or not (e.g., late vs. not late). You could then record the total number of deliveries made and the number recorded as late Or, you could record the number of people who call in sick on a particular day and the number of people scheduled to work each day Process Capability UNCLASSIFIED / FOUO 27
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UNCLASSIFIED / FOUO Capability Analysis for Attribute Data Use Capability Analysis (Binomial) if your data meet the following conditions: Each item is the result of identical conditions Each item can result in one of two possible outcomes (success/failure, go/no-go) The probability of a success (or failure) is constant for each item The outcomes of the items are independent of each other Process Capability UNCLASSIFIED / FOUO 28
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UNCLASSIFIED / FOUO Streamlining the RC ARFORGEN Progression Open the Minitab dataset BPCAPA1.MTW Background: You are a Brigade Operations Officer and you want to assess the overall readiness of your Brigade based on annual data from the Unit Status Report system. You focus in on the monthly reports from the past year and count the proportion of (defectives) units that were not meeting the required status for readiness. You want to assess “how capable and ready” your Brigade is for it‟s wartime or primary mission. Objective: Baseline the capability of the process Process Capability UNCLASSIFIED / FOUO 29
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UNCLASSIFIED / FOUO Streamlining the RC ARFORGEN Progression Dataset DEFINITION VARIABLE (reference: AR 220-1) CONTROL The aggregate number of required personnel, equipment on-hand, and the number of collective training events for that year, per unit. C-RAT The degree to which a unit has achieved prescribed levels of fill for personnel, equipment, the operational readiness status of available equipment, and the training proficiency status of the unit. S-RAT Equipment supply status of a unit – equipment on-hand is based on the quantity and type of required equipment that is available to the unit . P-RAT Personnel status of a unit – based on the number and type of required personnel available to the unit for the execution of the wartime or primary mission for which the unit is organized or designed. T-RAT Unit training status is based upon the unit commander’s assessment of the unit’s training proficiency on mission-essential tasks, the number of days required to achieve or sustain full mission-essential task proficiency. Process Capability UNCLASSIFIED / FOUO 30
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UNCLASSIFIED / FOUO Streamlining the RC ARFORGEN Progression Process Capability Analysis We will first determine the overall unit C-RAT process capability. Defectives: C-RAT Use Sizes in: CONTROL We can then follow the same steps for S-RAT, P- RAT, and T-RAT. Process Capability UNCLASSIFIED / FOUO 31
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UNCLASSIFIED / FOUOStreamlining the RC ARFORGEN Progression Stat>Quality Tools>Capability Analysis>Binomial Process Capability UNCLASSIFIED / FOUO 32
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UNCLASSIFIED / FOUOStreamlining the RC ARFORGEN Progression The defectives are “C-RAT” and the sample size is in “Control” 1. Double click on C-3 C-RAT to put it in the Defectives box 2. Double click on C-2 CONTROL to place it in the Use sizes in: box 3. Click on OK Process Capability UNCLASSIFIED / FOUO 33
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UNCLASSIFIED / FOUOStreamlining the RC ARFORGEN Progression Binomial Process Capability Analysis of C-RAT P C har t Rate of Defectives 40 0.4 U C L=0.3713 % Defective P r opor tion 0.3 _ 30 P =0.2738 0.2 LC L=0.1762 20 0.1 1 4 7 10 13 16 19 22 25 28 100 150 200 Sample Sample Size C umulative % Defective Dist of % Defective The „P-chart‟ details that the processtats S ummary S is Tar 32 in control, with an average proportion (using 95.0% confidence) 6.0 of 30 defectiveness at 27.38%. er C I: e: 27.38 Low This % Defectiv 4.5 % Defective 25.64 means that the ARFORGEN process is 29.16 28 U pper C I: Target: 0.00 3.0 being affected by variation withinCthe 256449 26 P P M Def: Low er I: 273772 1.5 variables that make up the C-RATC I: 291621 U pper 24 P rocess Z: 0.6014 (equipment, personnel, 25 training). 0.5487 and Low er C I: 0.0 5 10 15 20 0 6 12 18 24 30 36 Sample U pper C I: 0.6543 Process Capability UNCLASSIFIED / FOUO 34
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UNCLASSIFIED / FOUOStreamlining the RC ARFORGEN Progression Binomial Process Capability Analysis of C-RAT P C har t Rate of Defectives 40 The „Cumulative % 0.4 U C L=0.3713 % Defective P r opor tion Defective‟ chart 0.3 _ P =0.2738 30 verifies that enough 0.2 data was collected to LC L=0.1762 20 0.1 represent the16process.28 1 4 7 10 13 19 22 25 100 150 200 Sample Sample Size C umulative % Defective Dist of % Defective S ummary S tats Tar 32 6.0 (using 95.0% confidence) 30 % Defectiv e: 27.38 4.5 % Defective Low er C I: 25.64 U pper C I: 29.16 28 3.0 Target: 0.00 P P M Def: 273772 26 Low er C I: 256449 1.5 U pper C I: 291621 24 P rocess Z: 0.6014 0.0 5 10 15 20 25 Low er C I: 0.5487 0 6 12 18 24 30 36 Sample U pper C I: 0.6543 Process Capability UNCLASSIFIED / FOUO 35
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UNCLASSIFIED / FOUOStreamlining the RC ARFORGEN Progression Binomial Process Capability Analysis of C-RAT P C har t Rate of Defectives 40 0.4 U C L=0.3713 % Defective P r opor tion 0.3 _ 30 P =0.2738 0.2 LC L=0.1762 20 0.1 The1 „Rate 7of 10 Sample 19 22 25 details a random 4 Defectives‟ plot 28 13 16 100 150 Sample Size 200 distribution of data points, which means that the % defective is not influenced by the number of C umulative % Defective Dist of % Defective Tar items sampled. 32 S ummary S tats 6.0 (using 95.0% confidence) Finally, the „Dist of %Defective‟ chart efectiv e: the 30 %D details 27.38 4.5 % Defective Low er C I: 25.64 overall distribution of the % defective from the 28 U pper C I: 29.16 Target: 0.00 3.0 sample. P P M D ef: 273772 26 Low er C I: 256449 1.5 See Appendix for analysis of other variables. U pper C I: 291621 24 P rocess Z: 0.6014 0.0 5 10 15 20 25 Low er C I: 0.5487 0 6 12 18 24 30 36 Sample U pper C I: 0.6543 Process Capability UNCLASSIFIED / FOUO 36
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UNCLASSIFIED / FOUO Example Results The overall process is in control; hence, the data can be taken to the next phase on analysis. The voice of the process is suggesting that possible variables that require investigating are: equipment readiness and training readiness. Equipment readiness covers three sub-variables: Equipment that are mission capable (percentage) Pacing items that are mission capable (percentage) Overall equipment readiness rating Training readiness collectively looks at the overall training accomplishments of the unit (as determined by the unit commander). There are several factors bearing down on the process (possible “noise” in the system): Non-ARFORGEN training requirements (state mission) Overseas deployment training requirements – tasked by the higher HQ Theater Security Exercise requirements – tasked by the higher HQ Process Capability UNCLASSIFIED / FOUO 37
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UNCLASSIFIED / FOUO Binomial Capability Analysis – Data Display Binomial Process Capability Analysis of C-RAT P C har t Rate of Defectives 40 0.4 U C L=0.3713 % Defective P r opor tion 0.3 _ 30 P =0.2738 0.2 LC L=0.1762 20 0.1 1 4 7 10 13 16 19 22 25 28 100 150 200 Sample Sample Size Tests performed w ith unequal sample sizes C umulative % Defective H istogr am S ummary S tats Tar 32 6.0 (95.0% confidence) 30 % Defectiv e: 27.38 4.5 % Defective Fr equency Low er C I: 25.64 U pper C I: 29.16 28 3.0 Target: 0.00 P P M Def: 273772 26 Low er C I: 256449 1.5 U pper C I: 291621 24 P rocess Z: 0.6014 0.0 5 10 15 20 25 Low er C I: 0.5487 0 6 12 18 24 30 36 Sample U pper C I: 0.6543 % Defective Shows Percent Defective and Process Z (Sigma Level) UNCLASSIFIED / FOUO 38
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UNCLASSIFIED / FOUO Normal Capability Analysis – Display Options Normal Data UNCLASSIFIED / FOUO 39
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UNCLASSIFIED / FOUO Capability Analysis – Cpk or Z Bench? Process Capability of Delivery Time Process Capability of Delivery Time USL USL P rocess Data Within P rocess Data Within LS L * Ov erall LS L * Ov erall Target * Target * USL 30 P otential (Within) C apability USL 30 P otential (Within) C apability S ample M ean 29.1203 Cp * S ample M ean 29.1203 Z.Bench 0.31 S ample N 266 C PL * S ample N 266 Z.LS L * S tDev (Within) 2.87033 C P U 0.10 S tDev (Within) 2.87033 Z.U S L 0.31 S tDev (O v erall) 2.68901 C pk 0.10 S tDev (O v erall) 2.68901 C pk 0.10 O v erall C apability O v erall C apability Pp * Z.Bench 0.33 PPL * Z.LS L * PPU 0.11 Z.U S L 0.33 P pk 0.11 P pk 0.11 C pm * C pm * 24 26 28 30 32 34 36 24 26 28 30 32 34 36 O bserv ed P erformance E xp. Within P erformance E xp. O v erall P erformance O bserv ed P erformance E xp. Within P erformance E xp. O v erall P erformance P P M < LS L * PPM < LS L * P P M < LS L * % < LS L * % < LS L * % < LS L * P P M > U S L 281954.89 PPM > U S L 379619.67 P P M > U S L 371778.52 % > U S L 28.20 % > U S L 37.96 % > U S L 37.18 P P M Total 281954.89 PPM Total 379619.67 P P M Total 371778.52 % Total 28.20 % Total 37.96 % Total 37.18 Displays Cpk and Displays Benchmark Z PPM (Parts Per Million) (Sigma Level) and Percent above USL Enables comparison of process capability (SQL) between all processes no matter what kind of data UNCLASSIFIED / FOUO 40
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UNCLASSIFIED / FOUO Process Capability Template Process Capability of Workdays 118 data points collected Calculations Based on Lognormal Distribution Model Non-normal distribution LSL USL Mean = 44 days LS L P rocess Data 0 O v erall C apability Z.Bench -0.31 Target * Z.LS L 3.07 Lower Cust Spec = 0 days USL 15 Z.U S L -0.02 Upper Cust Spec = 15 days S ample M ean 44.8136 S ample N 118 - Example - P pk -0.01 E xp. O v erall P erformance Location 3.09501 % < LS L 0.00 S cale 1.26378 65% of observations % > U S L 62.03 O bserv ed P erformance % Total 62.03 outside customer spec % < LS L 0.00 % > U S L 65.25 Z Bench = -.31 % Total 65.25 0 60 120 180 240 300 360 420 Required Deliverable UNCLASSIFIED / FOUO 41
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UNCLASSIFIED / FOUO Exercise: Analyze Process Capability Objective Perform a process capability study for the GGAs Budget Department Instructions Identify Primary Y metric Determine customer specification limits Calculate Z Bench - Sigma Quality Level (SQL) Time = 15 Minutes UNCLASSIFIED / FOUO 42 2 4
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UNCLASSIFIED / FOUO Takeaways Once a process is in statistical control, you want to determine if it is capable; that it is meeting specification limits and producing “good” or satisfactory services or deliverables from the service process You determine capability by comparing the width of the process variation with the width of the specification limits Capability indices, Cp and Cpk, are ratios of the specification tolerance to the natural process variation, and are a straightforward way to assess process capability Because these indices are unitless, you can use capability statistics to compare the capability of one process to another Process Capability UNCLASSIFIED / FOUO 43
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UNCLASSIFIED / FOUO What other comments or questions do you have? UNCLASSIFIED / FOUO 44
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