生产过程控制教材.pptx

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1、Process Capability Cp/Cpk/Pp/Ppk Global Training MaterialGlobal Training MaterialCreator :Global Mechanics Process ManagerFunction :MechanicsApprover :Gary Bradley/Global Process TeamDocument ID :DMT00018-ENVersion/Status:V.1.0/ApprovedLocation :Notes:NMP DOCMANR4 PCP PC Process Library DocManChange

2、 History:IssueDateHandled By ments1.021st Dec01Jim Christy&Sren Lundsfryd Approved for Global UseNOTE All ments and improvements should be addressed to the creator of this document.ContentsSectionHeading/DescriptionPage1Variation,Tolerances and Dimensional Control42Population,Sample and Normal Distr

3、ibution153Cp and Cpk Concept284Use of the NMP Data Collection Spreadsheet445Confidence of Cpk52Process Capability-Evaluating Manufacturing VariationAcknowledgementsBenny MatthiassenNMP CMT,Copenhagen,DenmarkFrank AdlerNMP Alliance,Dallas,USAJoni LaaksoNMP R&D,Salo,FinlandJim ChristyNMP SRC,Southwood

4、,UKSection 1Variation,Tolerances and Dimensional ControlTwo Types of Product CharacteristicsVariable:A characteristic measured in physical units,e.g.millimetres,volts,amps,decibel and seconds.ONOFFAttribute:A characteristic that by comparison to some standard is judged“good”or“bad”,e.g.free from scr

5、atches(visual quality).In this training we deal with variables onlyThe Sources of Process/System VariationMethodsOperatorsCustomer SatisfactionMaterialEnvironmentEquipmentProcessTwo Types of ProcessesAll processes have:Natural random variability=due to mon causesStable Process:A process in which var

6、iation in out es arises only from mon causesUnstable Process:A process in which variation is a result of both mon and special causesUSLLSLnominal valueDefectUSLLSLnominal value Unnatural variability=due to special causesShewhart Shewhart 19311931 The Two Causes of Variation mon Causes:Causes that ar

7、e implemented in the process due to the design of the process,and affect all out es of the processIdentifying these types of causes requires methods such as Design of Experiment DOE,etc.Special Causes:Causes that are not present in the process all the time and do not affect all out es,but arise beca

8、use of specific circumstancesSpecial causes can be identified using Statistical Process Control SPCUSLLSLNominalvalueDefectUSLLSLnominal valueTolerancesLSL lower specification limit10,7USL upper specification limit10,9Acceptable partRejected PartRejected ProductNominal10,80,1Rejected PartA tolerance

9、 is a allowed maximum variation of a dimension.Measurement ReportIn most cases we measure only one part per cavity for measurement reportExample of Capability Analysis DataFor some critical dimensions we need to measure more than 1 partFor capability data we usually measure 5 pcs 2 times/hour=100 pc

10、s but sampling plan needs to be made on the basis of production quantity,run duration and cycle timeProcess Capability-What is it?Process Capability is a measure of the inherent capability of a manufacturing process to be able to consistently produce ponents that meet the required design specificati

11、onsProcess Capability is designated by Cp and CpkProcess Performance is a measure of the performance of a process to be able to consistently produce ponents that meet the required design specifications.Process Performance includes special causes of variation not present in Process CapabilityProcess

12、Performance is designated Pp and PpkWhy Make Process Capability StudiesLSL(lower specification limit)10,7USL(upper specification limit)10,9Nominal10,80,1This part is within spec.The tool would be approved if only this part was measuredThese parts are out of spec and could be approved if only one goo

13、d part was measuredA process capability study would reveal that the tool should not be acceptedWhen a dimension needs to be kept properly within spec,we must study the process capability.but still this is no guarantee for the actual performance of the process as it is only an initial capability stud

14、y E1.5 E1 E2 E3 E4 E5The Nokia Process Verification ProcessBlack diamonds to be fixed by E3(often a change of a white diamond)Proposal for black diamonds to be discussed with Supplier.Max:105,85Ongoing Process Control(SPC)Tolerances applied to drawingType 1 Functional Characteristics-1 part/cavity m

15、easured for measurement reportWhite diamonds(s)to be agreedWhite diamonds(s)to be discussed with supplier10 parts/cavity measured for measurement reportCapability study:Requirement:Cp and Cpk 1.67 by E3.Quantities to be agreed with supplier.Minimum 5 parts pr 1/2 hour in 10 hours measured for each c

16、avity=100 parts.Can vary depending on tool capacity,e.g.stamped parts(see DMY00019-EN)Section 2.Population,Sample and Normal DistributionThe Bell Shaped Normal DistributionSymmetrical shape with a peak in the middle of the range of the data.Indicates that the input variables Xs to the process are ra

17、ndomly influenced.“Population Parameters=Population mean=Population standard deviationPopulation versus SamplePopulationAn entire group of objects that have been made or will be made containing a characteristic of interestSampleThe group of objects actually measured in a statistical studyA sample is

18、 usually a subset of the population of interestPopulationSample“Sample Statistics”x=Sample means=Sample standard deviationThe Normal DistributionWhat Measurements Can Be Used to Describe a Process or System?Example:x1 =5x2 =7x3 =4x4 =2x5 =6mean(average)or describes the location of the distribution(m

19、),a measure of central tendency,is the mean or average of all values in the population.When only a sample of the population is being described,mean is more properly denoted as (x-bar):Example:x1 =5x2 =7x3 =4x4 =2x5 =6The most simple measure of variability is the range.The range of a sample is define

20、d by as the difference between the largest and the smallest observation from samples in a sub-group,e.g.5 consecutive parts from the manufacturing process.What Measurements Can Be Used to Describe Process variation?sST-often notated as or sigma,is another measure of dispersion or variability and sta

21、nds for“short-term standard deviation,which measures the variability of a process or system using“rational sub-grouping.where is the range of subgroup j,N the number of subgroups,and d2*depends on the number N of subgroups and the size n of a subgroup(see next slide)What Measurements Can Be Used to

22、Describe Process variation?d2*values for SSTWhere:N=no.of sub-groups,n=no.of samples in each sub-groupd d2 2*d d2 2Typical:N=20&n=5x x3 3x x2 2x x1 1x x1010 x x_ _t tExample:What Measurements Can Be Used to Describe Process variation?The Difference Between SST and sLT!meanTimeDimensionShort term Sta

23、ndard DeviationLong term Standard DeviationSubgroup size n=5Number of subgroups N=7TRENDSubgroup No.1The difference between the standard deviations sLT and sST gives an indication of how much better one can do when using appropriate production control,like Statistical Process Control SPC.Short-term

24、standard deviation:Long-term standard deviation :The difference between sST and sLTThe difference between sST and sLTThe difference between sLT and sST is only in the way that the standard deviation is calculatedsLT is always the same or larger than sSTIf sLT equals sST,then the process control over

25、 the longer-term is the same as the short-term,and the process would not benefit from SPCIf sLT is larger than sST,then the process has lost control over the longer-term,and the process would benefit from SPCThe reliability of sLT is improved if the data is taken over a longer period of time.Alterna

26、tively sLT can be calculated on several occasions separated by time and the results pared to see whether sLT is stableExercise 1:Sample Distributions1.In Excel file Data exercise 1.xls you find 100 measurements being the result of a capability study.The specification for the dimension is 15,16,01 2.

27、How well does the sample population fit the specification,e.g.should we expect any parts outside spec?3.Mention possible consequences of having a part outside spec.4.Mention possible causes of variation for parts.5.Calculate the sample mean and sample standard deviation for the 100 measurements.Use

28、the average and stdev functions Excel.Section 3.Cp and Cpk ConceptDefining Cp and PpSample meanProcess variation 6*s USL-LSLLSL USLNominal dimThe tolerance area divided by the total process variation,irrespective of process centring.Defining Cpk and PpkSample meanProcess variation 3sProcess variatio

29、n 3sMean-LSLUSL-MeanLSL USLNominal dimCpk and Ppk Indexes account also for process centring.What is the Difference Between Cp and Cpk?The Cp index only accounts for process variabilityThe Cpk Index accounts for process variability and centering of the process mean to the design nominal Therefore,Cp

30、CpkNOTE:Same applies also for Pp and PpkCp=Cpk(both low)LSLUSLMean=NominalReject partsReject partsCp high,Cpk low Process should be optimized!NominalLSLMeanUSLReject partsWhat Do These Indexes Tell Us?Simple numerical values to describe the quality of the process The higher the number the betterRequ

31、irement for Cp and Cpk is 1.67 min.Re mendation for Pp and Ppk is 1.33 min.This leaves us some space for the variation,i.e.a safety marginAre we able to improve our process by using SPC?If index is low,following things should be given a thought:Is the product design OK?Are tolerance limits set corre

32、ctly?Too tight?Is the process capable of producing good quality products?Process variation?DOE required?Is the measuring system capable?See Gage R&RCpk-With a 2-sigma safety margin-3 sST+3 sSTLCLUCLLSLUSLMean value=Nominal value or TargetRequirement for Cp and Cpk is 1.67 min.1.67 is a ratio of=5/3

33、or 10/6.6*standard deviation10*standard deviation2*standard deviation2*standard deviationCpk=1.67 the process is CAPABLECpk=2.0 the process has reached Six Sigma levelWhat Do These Indexes Tell Us?If Cp=Cpk,If Pp=Ppk,If Cpk Cp,If Ppk Pp,If Cp=Pp,If Cpk=Ppk,If Pp Cp,If Ppk Cpk,then process is affecte

34、d by special causes.Investigate X-bar/R-chart for out-of-control conditions.SPC may be effective then process is not affected by special causes during the study run.SPC would not be effective in this case then process perfectly centred then process not centred check process mean against design nomin

35、alCp and Cpk Indices and Defectsboth tails of the normal distributionboth tails of the normal distributionPp=Ppk=1,33 63 ppm defects=0,006%Cp=Cpk=1,67 0,6 ppm defects=0,00006%Note:Ppm reject rates calculated from Cp&Cpk are based on the short term variation which may not represent the long term reje

36、ct rate The Effects of Cpk and Cp on FFRExercise 2:Cp and CpkCalculate Cp and Cpk for the 100 measurements in the file Data exercise 1.xlsDetermine the approximate Cp and Cpk for the 4 sample populations on the following pageShould actions be made to improve these processes.If yes,which?Estimate Cp

37、and Cpk?The width of the normal distributions shown include 3*sLSLUSLA)LSLUSLB)LSLUSLC)USLLSLD)Estimate Cp and Cpk?-ALSLUSLA Mean and nominalUSL-LSL6*sUSL-MeanMean-LSL3*sEstimate Cp and Cpk?-BLSLUSLB NominalMeanUSL-LSL6*sUSL-MeanMean-LSL3*sEstimate Cp and Cpk?-CLSLUSLC NominalMeanUSL-LSL6*sUSL-MeanM

38、ean-LSL3*sEstimate Cp and Cpk?-DUSLLSLD NominalMeanUSL-LSL6*sUSL-MeanMean-LSL3*sSection 4.Use of the NMP Data Collection SpreadsheetExample of how to Collect Data 1.Run in and stabilise process2.Note the main parameters for reference3.When the process is stable run the tool for 10 hours3.Take 5 part

39、s out from each cavity every half hour and mark them with time,date and cavity.Total 20 sets of 5 parts from each cavity must be made,or according to agreement.4.After the last sample lot note the main process parameters for reference5.Measure and record the main functional characteristics white dia

40、monds 6.Fill data into the NMP data collection spreadsheet7.Analyse!See DMY 00019-ENClassification and Marking of Functional CharacteristicsTimeDimensionSubgroup size n=5Number of subgroups N=200,5 hours between samples takenNote:For clarity,only 6 subgroups are shownData Collection Sheet DMM00024-E

41、N-5.0 Data Collection Sheet DMM00024-EN-5.0 Graphical Presentation:HistogramWhat kind of distribution?Location versus tolerance area Width deviationExample:Cp2.59 Pp1.86Cpk0.88 Ppk0.63Graphical Presentation:X-bar and R-ChartX-Bar ChartR-ChartGraphical Presentation-Time Series PlotSomething happened

42、here!Exercise 3:Cpk Data SpreadsheetOpen spreadsheet Data exercice 3.xls.Dim 13 is identical to the data from the previous exercises.Verify the results from the previous exercises for dimension 13.Analyse the remaining data sets an ment the process,should any actions be made?Remember to create and l

43、ook at the charts.Section 5.Confidence of CpkConfidence of CpkCpk values are not definite numbers as they are based on relatively small samples of a population.The 95%confidence interval determines the interval which includes the true Cpk value with a probability of 95%,i.e.there is a probability of

44、 5%that Cpk is either lower or higher than this confidence interval.95%confidence intervalActual cpkCpk upper confidence limitCpk lower confidence limitConfidence of CpkSmall sample sizes gives wide confidence intervalsCpk Confidence Limits with a sample size of 100 and a nominal Cpk of 1.67演讲完毕，谢谢观看！