1、1 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialCreator :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 History:Iss
2、ueDateHandled ByComments1.021st Dec01Jim Christy&Sren LundsfrydApproved 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 ChristyCompany ConfidentialSectionHeading/DescriptionPage1Variation,Tolerances and Di
3、mensional 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 ConfidentialAcknowledgementsBenny Matthiassen(NMP CMT,Copenhagen,Denmark)Frank Adler(NMP Allian
4、ce,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 ConfidentialVariation,Tolerances and Dimensional Control5 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialVariable:A characteristic measured in
5、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 scratches(visual quality).In this training we deal with variables only6 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confid
6、entialMethodsOperatorsCustomer SatisfactionMaterialEnvironmentEquipmentProcess7 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidential All processes have:Natural(random)variability=due to common causes Stable Process:A process in which variation in outcomes arises only from common cause
7、s Unstable Process:A process in which variation is a result of both common and special causesUSLLSLnominal valueDefectUSLLSLnominal value Unnatural variability=due to special causes8 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidential Common Causes:Causes that are implemented in the
8、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
9、circumstancesSpecial causes can be identified using Statistical Process Control(SPC)USLLSLNominalvalueDefectUSLLSLnominal value9 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialLSL(lower specification limit)10,7USL(upper specification limit)10,9Acceptable partRejected PartRejected
10、 ProductNominal10,80,1Rejected PartA tolerance is a allowed maximum variation of a dimension.10 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialIn most cases we measure only one part per cavity for measurement report11 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confide
11、ntial For some critical dimensions we need to measure more than 1 part For 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)1st Subgroup2nd Subgroup3rd Subgroup4th Subgroup118.53118.52118.
12、54118.56118.54118.54118.52118.55118.51118.51118.50118.55118.53118.51118.52118.55118.51118.54118.54118.555th Subgroup6th Subgroup7th Subgroup8th Subgroup118.55118.54118.57118.60118.54118.56118.56118.57118.55118.55118.57118.55118.54118.54118.55118.56118.56118.53118.54118.559th Subgroup10th Subgroup 11
13、th Subgroup 12th Subgroup118.60118.61118.58118.60118.59118.60118.60118.63118.58118.61118.61118.63118.60118.59118.60118.61118.59118.59118.59118.6412 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidential Process Capability is a measure of the inherent capability of a manufacturing proces
14、s to be able to consistently produce components that meet the required design specifications Process Capability is designated by Cp and Cpk Process Performance is a measure of the performance of a process to be able to consistently produce components that meet the required design specifications.Proc
15、ess Performance includes special causes of variation not present in Process Capability Process Performance is designated Pp and Ppk13 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialLSL(lower specification limit)10,7USL(upper specification limit)10,9Nominal10,80,1This part is with
16、in spec.The tool would be approved if only this part was measuredThese parts are out of 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 pr
17、ocess capability.but still this is no guarantee for the actual performance of the process as it is only an initial capability study14 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidential E1.5 E1 E2 E3 E4 E5Black diamonds to be fixed by E3(often a change of a white diamond)Proposal for
18、 black diamonds to be discussed with Supplier.Max: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 meas
19、urement 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 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 ChristyCo
20、mpany Confidential16 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidential Symmetrical 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-Dec-2001/Jim ChristyCompany Confide
21、ntial“Population Parameters”=Population mean=Population standard deviationPopulation An entire group of objects that have been made or will be made containing a characteristic of interestSample The group of objects actually measured in a statistical study A sample is usually a subset of the populati
22、on of interestPopulationSample“Sample Statistics”x=Sample means=Sample standard deviation18 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidential19 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialxxxxNN12.Example:x1 =5x2 =7x3 =4x4 =2x5 =68.4524562475x mean(average)or
23、 describes the location of the distributionx (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 described,mean is more properly denoted as (x-bar):x20 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidenti
24、al),.,min(),.,max(2121NNxxxxxxRExample:x1 =5x2 =7x3 =4x4 =2x5 =6527)6,2,4,7,5min()6,2,4,7,5max(RThe 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 observation from samples in a sub-group,e.g.5 consecutive par
25、ts from the manufacturing process.21 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialsST-often notated as or sigma,is another measure of dispersion or variability and stands for“short-term standard deviation”,which measures the variability of a process or system using“rational”sub
26、-grouping.sRNdRdS TjjN122*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)RXXjjjmaxmin22 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialWhere:N=no.of sub-groups,n=no.of samples in e
27、ach sub-groupTypical:N=20&n=523 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidential 1)(.)()(222212NxxxxxxssNLTLT92.17.315)8.46()8.42()8.44()8.47()8.45(22222LTsExample:24 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialmeanTimeDimensionShort term Standard DeviationL
28、ong term Standard DeviationSubgroup size n=5Number of subgroups N=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 co
29、ntrol,like Statistical Process Control(SPC).sxxxxxxNLTN()().()122221sRNdRdS TjjN122*Short-term standard deviation:Long-term standard deviation26 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialThe difference between sLT and sST is only in the way that the standard deviation is cal
30、culatedsLT is always the same or larger 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
31、SPCThe reliability of sLT is improved 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 Confidential1.In Excel fil
32、e 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.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
33、.4.Mention 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 Confidential29 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompa
34、ny ConfidentialSample meanProcess variation 6*sstpsLSLUSLC*6-USL-LSLLSL USLNominal dimltpsLSLUSLP*6-The tolerance area divided by the total process variation,irrespective of process centring.30 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialststpksmeanUSLsLSLmeanC*3-,*3-minSample
35、 meanProcess variation 3sProcess variation 3sMean-LSLUSL-MeanLSL USLNominal dimltltpksmeanUSLsLSLmeanP*3-,*3-minCpk and Ppk Indexes account also for process centring.31 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidential The Cp index only accounts for process variability The Cpk Inde
36、x accounts for process variability and centering of the process mean to the design nominal Therefore,Cp Cpk NOTE: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 T0001801.P
37、PT/21-Dec-2001/Jim ChristyCompany ConfidentialSimple 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 variation,i.e.a safety marginAre we able to
38、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 measuring system capable?(See Gage R&R)33
39、NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidential-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 deviation2*standard deviation2*standard deviation34 NOKIA 2001 T0001801.P
40、PT/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 ConfidentialIf 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 affected b
41、y 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 nominal)
42、36 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialCpk/PpkCp/Pp0.10.20.30.40.50.60.70.80.91.01.11.21.331.41.51.672.02.53.04.0%/PPM0.176.4256.6144.8940.0038.5638.2638.2138.2138.2138.2138.2138.2138.2138.2138.2138.2138.2138.2138.2138.21%0.254.8638.9331.0228.2527.5627.4427.4327.4327.4
43、327.4327.4327.4327.4327.4327.4327.4327.4327.4327.43%0.336.8125.0920.1918.7518.4518.4118.4118.4118.4118.4118.4118.4118.4118.4118.4118.4118.4118.41%0.423.0115.1012.3311.6411.5211.5111.5111.5111.5111.5111.5111.5111.5111.5111.5111.5111.51%0.513.368.477.036.736.696.686.686.686.686.686.686.686.686.686.686
44、.68%0.67.194.413.733.613.593.593.593.593.593.593.593.593.593.593.59%0.73.572.131.831.791.791.791.791.791.791.791.791.791.791.79%0.81.640.950.840.820.820.820.820.820.820.820.820.820.82%0.90.690.400.350.350.350.350.350.350.350.350.350.35%1.027001509136313501350135013501350135013501350PPM1.196753248548
45、4483483483483483483PPM1.2318165160159159159159159159PPM1.336338333332323232PPM1.427141313131313PPM1.5733333PPM1.670.60.30.30.30.3PPM2.00.00.00.00.0PPM2.50.00.00.0PPM3.00.00.0PPM4.00.0PPMPp=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
46、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 ConfidentialCpkCpPpm defectsTotal number of defects for 50,000,000 partsTotal number of defects if phone has 10 of these parts0.81.338,200410,0004,100,000
47、11.331,35067,500675,0001.331.33633,15031,5001.331.67331,65016,5001.501.5073503,5001.671.671303002.002.0000138 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidential Calculate Cp and Cpk for the 100 measurements in the file Data exercise 1.xls Determine the approximate Cp and Cpk for the
48、 4 sample populations on the following page Should actions be made to improve these processes.If yes,which?39 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialThe width of the normal distributions shown include 3*sLSLUSLA)LSLUSLB)LSLUSLC)USLLSLD)40 NOKIA 2001 T0001801.PPT/21-Dec-20
49、01/Jim ChristyCompany ConfidentialLSLUSLA)Mean and nominalUSL-LSL6*sUSL-MeanMean-LSL3*s41 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialLSLUSLB)NominalMeanUSL-LSL6*sUSL-MeanMean-LSL3*s42 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialLSLUSLC)NominalMeanUSL-LS
50、L6*sUSL-MeanMean-LSL3*s43 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany ConfidentialUSLLSLD)NominalMeanUSL-LSL6*sUSL-MeanMean-LSL3*s44 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidential45 NOKIA 2001 T0001801.PPT/21-Dec-2001/Jim ChristyCompany Confidential1.Run in and stabil
