1、ProcessControlTaking the mystery out of CpkBest Practices for the Use of CpkStatisticsStatisticsGoal & OutlineGoal:Describe the concept and proper use ofCpk. Dispel myths, misuse and confusionabout Cpk.Outline1. Introduction2. Definition of Terms3. Best Practices for Using Cpk4. Top Ten Most Confusi
2、ng Things about Cpk5. SummaryDefinition of TermsCapability - The ability of a process to produce parts within specification.A process is said to be capable when nearly all parts produced by the process are within specification.Process Capability Indices - Measures of the capability of a process.X- T
3、he average of a sample of data,- The sample standard deviationSUSL, LSL = Upper and Lower specificationxxni=sxxni=-()21Cp - =USLLSLs6CpkXsXs=minimum,USL - 3- LSL3Cp & Cpk: ConceptProcess WidthToleranceCpCp is a ratio of the process width (6 sigma) to the specification tolerance width (USL-LSL)1/2 Pr
4、ocess WidthDistance from Spec Limit to Process MeanCpkWorst case ratioCpk is a ratio of 1/2 the process width (3 sigma) to distance from the spec limit to the process average (mean)Cp & Cpk: ConceptCp = 1Cpk = 1Cp = 1Cpk = 1Cpk = 2LSLUSLLSLUSLLSLUSLLSLUSLLSLUSLWhy use Cpk?Cpk.5.75.91.01.151.301.331.
5、523% or ppm13%2.4%0.7%2700 ppm561 ppm96 ppm66 ppm7ppm2ppb 1ppbSingle number summary of process performance. Can compare Performance across Processes Motivates variance reduction and process centering. Distinguishes among in-spec processes.Cpk can be converted to an estimated defect rate for normally
6、 distributed processes. (These numbers assume a stable, centered process)Proper Use of CpkAssumptions1. The process is statistically stable2. Data is distributed approximately normally.3. Specifications represent customer needs.4. Process target is centered between specs.5. Measurement variation is
7、small.More On Assumptions 1. -The data collected should exhibit stability when plotted on a control chart-Cpk of the unstable process may be representative of the historical performance of the process and not necessarily indicative of the ability of te process to meet the specs in the longer term2.
8、Because- Cpk for the non normal process misrepresents the process due to the effect that non normality has some estimation3. Specification limits used for calculating Cpk may be arbitraryCpk may be good, quality of product could be badCpk may be bad, quality of product could be goodSpecs may be “bes
9、t guesses” or based on processChanging specs causes Cpk to change, while the performance of the process in unchanged.More on Assumptions4. The target needs to be the center of the spec limits If the target is not the center of the spec limits, then the process mean must be located in the interval ta
10、rget-(spec range)/6 to target+(spec range)/65. The measurements variation in the values used for calculating the Cpk must be small relative to the specific process capability for the parameter being measured.If the measurement variation is comparatively large, then the Cpk may not be indicative. Bec
11、ause Cpk will be including this variation, which is not related to the ability of thew process to meet the specificationsProper Use of CpkCalculating and Interpreting CpkCollect at least 100 measurements over an extended time period, (2-4 weeks or more).Validate the assumptions (above).Calculate Cpk
12、 using the overall standard deviation of the individual data. Dont use subgroup averages or pooled standard deviation!Calculate a confidence interval for Cpk (especially if n 100).Make a capability plot (histogram with overlaid spec limits).Resolve any differences.Top 10 List of Misuse and Confusion
13、1. People think Cpk is the only measure that matters!2. There is no agreement on which Cpk value is good. (1, 1.15, 1.33, 1.5, 2, etc.).3. Specification limits used for Cpk may be arbitrary.4. There are too many variations on the Cpk theme.5. People dont graph their data when interpreting Cpk.6. The
14、 scale of Cpk is non-characteristic.7. Cpk is inappropriately used as a control parameter.8. The Cpk estimate for small samples is regarded as the truth.9. Cpk misrepresents non-normal or unstable processes.10. The use of Cpk is mandated without proper training.Reason #10 The use of Cpk is mandated
15、without proper training.Used in situations where it doesnt fit.Calculated just for management without any benefit to those who manage the process.Reason #9Cpk misrepresents non-normal or unstable processes.0510LSLUSLCpk is 0.3, should it be 1.0?Cpk = 1, Instability is hiddenLSLUSLCpk is 1.0, should
16、it be 0.5?Reason #8The Cpk estimate for small samples is regarded as the truth.Sample Scenario250,000 pens/month, True Cpk = 1.31.31.3n=25n=200sample Cpksample CpkRepeated SamplesRepeated SamplesReason #7Cpk is used as a control parameter.CpkYieldPeople see this.and think this.Cpk is not a good shor
17、t-term control parameter.Reason #6The scale of Cpk is non-intuitive. 01.51.3PoorAcceptableExcellent2.0Cpk ScaleReason #5People dont graph their data when interpreting Cpk. Reason #4There are too many variations on the Cpk theme. Cp, Cpk, Cpu, Cpl, Cpm, Cpmk, Cpsk, . Automotive Industry Action Group
18、(A.I.A.G.)Introduced Pp and PpkRedefined Cpk (Ppk is the same as old Cpk)!Short Term vs. Long TermCapability indices vs. Performance indicesANSI, ASQC, ISO, ?Reason #3Specification limits used for Cpk may be arbitrary. Cpk may be good - Quality of product could be badSpecs are in some instances just
19、 best guessesChanging specifications causes Cpk to change, while the performance of the process is unchanged.Reason #2There is no agreement on which Cpk value is goodCpk = 1.15LSLUSLCpk = 2LSLUSLCpk = 1LSLUSLCpk = 1.5LSLUSLCpk = 1.3LSLUSL?The #1 ReasonPeople think Cpk is the only measure that matter
20、s!CpkControl ChartsStabilityDistribution ShapeActual YieldPareto of DefectsMeasurement CapabilityValidate Specs to Customer NeedsAverage (Mean)Standard DeviationMinimum (smallest measurement)Maximum (largest measurement)Reality is more complicated!Remain an important tool for summarizing process performance and communicating with management.Expect more confusion as alternate definitions are proposed.Attempts to simplify Cpk (including this presentation) will cause short term confusion.External training offerings will continue the trend toward complicating CpkFuture of Cpk
