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1、1 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialProcess 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/App
2、rovedLocation :Notes:NMP DOCMANR4 PCP PC Process Library DocManChange History:IssueDateHandled ByComments1.021st Dec01Jim Christy&Sren Lundsfryd Approved for Global UseNOTE All comments and improvements should be addressed to the creator of this document.2 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim Chr
3、istyCompany ConfidentialContentsSectionHeading/DescriptionPage1Variation,Tolerances and Dimensional Control42Population,Sample and Normal Distribution153Cp and Cpk Concept284Use of the NMP Data Collection Spreadsheet445Confidence of Cpk523 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confi
4、dentialProcess Capability-Evaluating Manufacturing VariationAcknowledgementsBenny Matthiassen(NMP CMT,Copenhagen,Denmark)Frank Adler(NMP Alliance,Dallas,USA)Joni Laakso(NMP R&D,Salo,Finland)Jim Christy(NMP SRC,Southwood,UK)4 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialSection
5、1Variation,Tolerances and Dimensional Control5 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialTwo Types of Product CharacteristicsVariable:A characteristic measured in physical units,e.g.millimetres,volts,amps,decibel and seconds.ONOFFAttribute:A characteristic that by comparison
6、 to some standard is judged“good”or“bad”,e.g.free from scratches(visual quality).In this training we deal with variables only6 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialThe Sources of Process/System VariationMethodsOperatorsCustomer SatisfactionMaterialEnvironmentEquipmentPr
7、ocess7 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialTwo Types of ProcessesAll processes have:Natural(random)variability=due to common causesStable Process:A process in which variation in outcomes arises only from common causesUnstable Process:A process in which variation is a r
8、esult of both common and special causesUSLLSLnominal valueDefectUSLLSLnominal value Unnatural variability=due to special causes8 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialShewhart(1931)Shewhart(1931)The Two Causes of VariationCommon Causes:Causes that are implemented in the
9、process due to the design of the process,and affect all outcomes 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 outcomes,but arise because of specific
10、circumstancesSpecial causes can be identified using Statistical Process Control(SPC)USLLSLNominalvalueDefectUSLLSLnominal value9 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialTolerancesLSL(lower specification limit)10,7USL(upper specification limit)10,9Acceptable partRejected Pa
11、rtRejected ProductNominal10,80,1Rejected PartA tolerance is a allowed maximum variation of a dimension.10 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialMeasurement ReportIn most cases we measure only one part per cavity for measurement report11 NOKIA 2001 T0001801.PPT/21-Dec-200
12、1/Jim ChristyCompany ConfidentialExample 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 pcs(but sampling plan needs to be made on the basis of production quantity,run duration and cycle time)12
13、NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialProcess Capability-What is it?Process Capability is a measure of the inherent capability of a manufacturing process to be able to consistently produce components that meet the required design specificationsProcess Capability is desig
14、nated by Cp and CpkProcess Performance is a measure of the performance of a process to be able to consistently produce components that meet the required design specifications.Process Performance includes special causes of variation not present in Process CapabilityProcess Performance is designated P
15、p and Ppk13 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialWhy 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
16、 spec and could be approved if only one good 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 proce
17、ss as it is only an initial capability study14 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidential 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
18、:105,85Ongoing Process Control(SPC)Tolerances applied to drawingType 1 Functional Characteristics-1 part/cavity measured 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
19、 Cpk 1.67 by E3.Quantities to be agreed with supplier.Minimum 5 parts pr 1/2 hour in 10 hours measured for each cavity=100 parts.Can vary depending on tool capacity,e.g.stamped parts(see DMY00019-EN)15 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialSection 2.Population,Sample and
20、 Normal Distribution16 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialThe 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 randomly influenced.17 NOKIA 2001 T0001801.PPT/21
21、-Dec-2001/Jim ChristyCompany Confidential“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 stat
22、istical studyA sample is usually a subset of the population of interestPopulationSample“Sample Statistics”x=Sample means=Sample standard deviation18 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialThe Normal Distribution19 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Con
23、fidentialWhat 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),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 des
24、cribed,mean is more properly denoted as (x-bar):20 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialExample:x1 =5x2 =7x3 =4x4 =2x5 =6The most simple measure of variability is the range.The range of a sample is defined by as the difference between the largest and the smallest observ
25、ation from samples in a sub-group,e.g.5 consecutive parts from the manufacturing process.What Measurements Can Be Used to Describe Process variation?21 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialsST-often notated as or sigma,is another measure of dispersion or variability and
26、 stands 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 Use
27、d to Describe Process variation?22 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidentiald2*values for SSTWhere:N=no.of sub-groups,n=no.of samples in each sub-groupd d2 2*d d2 2Typical:N=20&n=523 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidential x x3 3 x x2 2 x x1 1 x
28、x1010 x x_ _t tExample:What Measurements Can Be Used to Describe Process variation?24 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialThe Difference Between SST and sLT!meanTimeDimensionShort term Standard DeviationLong term Standard DeviationSubgroup size n=5Number of subgroups N
29、=7TRENDSubgroup No.125 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialThe 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 standard d
30、eviation:Long-term standard deviation :The difference between sST and sLT26 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialThe 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 la
31、rger than sSTIf sLT equals sST,then the process control over 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 improv
32、ed if the data is taken over a longer period of time.Alternatively sLT can be calculated on several occasions separated by time and the results compared to see whether sLT is stable27 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialExercise 1:Sample Distributions1.In Excel file Da
33、ta exercise 1.xls you find 100 measurements being the result of a capability study.The specification for the dimension is 15,16,01 2.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.M
34、ention possible causes of variation for parts.5.Calculate the sample mean and sample standard deviation for the 100 measurements.Use the average and stdev functions Excel.28 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialSection 3.Cp and Cpk Concept29 NOKIA 2001 T0001801.PPT/21-D
35、ec-2001/Jim ChristyCompany ConfidentialDefining Cp and PpSample meanProcess variation 6*s USL-LSLLSL USLNominal dimThe tolerance area divided by the total process variation,irrespective of process centring.30 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialDefining Cpk and PpkSamp
36、le meanProcess variation 3sProcess variation 3sMean-LSLUSL-MeanLSL USLNominal dimCpk and Ppk Indexes account also for process centring.31 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialWhat is the Difference Between Cp and Cpk?The Cp index only accounts for process variabilityThe
37、 Cpk Index accounts for process variability and centering of the process mean to the design nominal Therefore,Cp CpkNOTE:Same applies also for Pp and PpkCp=Cpk(both low)LSLUSLMean=NominalReject partsReject partsCp high,Cpk low Process should be optimized!NominalLSLMeanUSLReject parts32 NOKIA 2001 T0
38、001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialWhat Do These Indexes Tell Us?Simple numerical values to describe the quality of the process The higher the number the betterRequirement for Cp and Cpk is 1.67 min.Recommendation for Pp and Ppk is 1.33 min.This leaves us some space for the variat
39、ion,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 correctly?Too tight?Is the process capable of producing good quality products?Process variation?DOE required?Is the meas
40、uring system capable?(See Gage R&R)33 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialCpk-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 or 10/6.6*standard deviation10*standard dev
41、iation2*standard deviation2*standard deviation34 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialCpk=1.67 the process is CAPABLECpk=2.0 the process has reached Six Sigma level35 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialWhat Do These Indexes Tell Us?If Cp=
42、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 affected 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 cas
43、e then process perfectly centred then process not centred(check process mean against design nominal)36 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialCp and Cpk Indices and Defects(both tails of the normal distribution)(both tails of the normal distribution)Pp=Ppk=1,33 63 ppm def
44、ects=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 reject rate 37 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialThe Effects of Cpk and Cp on FFR38 NOKIA 2001 T000
45、1801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialExercise 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?
46、39 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialEstimate Cp and Cpk?The width of the normal distributions shown include 3*sLSLUSLA)LSLUSLB)LSLUSLC)USLLSLD)40 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialEstimate Cp and Cpk?-A)LSLUSLA)Mean and nominalUSL-LS
47、L6*sUSL-MeanMean-LSL3*s41 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialEstimate Cp and Cpk?-B)LSLUSLB)NominalMeanUSL-LSL6*sUSL-MeanMean-LSL3*s42 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialEstimate Cp and Cpk?-C)LSLUSLC)NominalMeanUSL-LSL6*sUSL-MeanMean-L
48、SL3*s43 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialEstimate Cp and Cpk?-DUSLLSLD)NominalMeanUSL-LSL6*sUSL-MeanMean-LSL3*s44 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialSection 4.Use of the NMP Data Collection Spreadsheet45 NOKIA 2001 T0001801.PPT/21-Dec
49、-2001/Jim ChristyCompany ConfidentialExample 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 parts out from each cavity every half hour and mark them with time,date and cavity.Total 20 sets of
50、 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 diamonds)6.Fill data into the NMP data collection spreadsheet7.Analyse!See DMY 00019-ENClassificat