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1、1 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialProcess Capability (Cp / Cpk / Pp / Ppk)Global Training MaterialCreator : Global Mechanics Process ManagerFunction : MechanicsApprover : Gary Bradley / Global Process TeamDocument ID : DMT00018-ENVersion / Status : V.1.0 / Appro
2、vedLocation : Notes : NMP DOCMANR4 PCP PC Process Library DocManChange History :IssueDateHandled 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 / J
3、im ChristyCompany 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 Christy
4、Company ConfidentialProcess 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 ChristyCom
5、pany ConfidentialSection 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:
6、 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 ConfidentialThe Sources of Process/System VariationMethodsOperatorsCustomer
7、 SatisfactionMaterialEnvironmentEquipmentProcess7 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 causesUn
8、stable 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 ConfidentialShewhart (1931)Shewhart (1931)The Two Causes of V
9、ariationCommon Causes: Causes that are implemented in the 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
10、 and do not affect all outcomes, but arise because of specific circumstancesSpecial causes can be identified using Statistical Process Control (SPC)USLLSLNominalvalueDefectUSLLSLnominal value9 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialTolerancesLSL (lower specification li
11、mit)10,7USL (upper specification limit)10,9Acceptable partRejected PartRejected 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 par
12、t per cavity for measurement report11 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / 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
13、 be made on the basis of production quantity, run duration and cycle time)12 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
14、components that meet the required design specificationsProcess Capability is designated 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 cause
15、s of variation not present in Process CapabilityProcess Performance is designated Pp 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 wit
16、hin 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
17、 process 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 E5The Nokia Process Verification ProcessBlack diamonds to be fixed by E3 (
18、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 measured for measurement reportWhite diamonds(s) to be agreedWhite diamonds(s) to be disc
19、ussed 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 cavity = 100 parts. Can vary depending on tool capacity, e.g. stamped parts (see DMY
20、00019-EN)15 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialSection 2.Population, Sample and 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
21、 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 Confidential“Population Parameters = Population mean = Population standard deviationPopulation versus SamplePopulationAn entire group of objects
22、that have been made or will be made containing a characteristic of interestSampleThe group of objects actually measured in a statistical studyA sample is usually a subset of the population of interestPopulationSample“Sample Statisticsx = Sample means = Sample standard deviation18 NOKIA 2001 T0001801
23、.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialThe Normal Distribution19 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialWhat Measurements Can Be Used to Describe a Process or System ?Example: x1 = 5x2 = 7x3 = 4x4 = 2x5 = 6mean (average) or describes the location of the dis
24、tribution (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) :20 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialExample: x1 = 5x2 = 7x3 =
25、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 observation from samples in a sub-group, e.g. 5 consecutive parts from the manufacturing process. What Measurements Can Be Used to Describe Pro
26、cess 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 stands for “short-term standard deviation, which measures the variability of a process or system using “rational sub-grouping.w
27、here 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 Describe Process variation?22 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany Confidentiald2* values for SS
28、TWhere: N = no. of sub-groups, n = no. of samples in each sub-groupd2*d2*d2d2Typical: N=20 & n=523 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany Confidential x3x3 x2x2 x1x1 x10x10x x_ _t tExample:What Measurements Can Be Used to Describe Process variation?24 NOKIA 2001 T0001801.PPT/ 21-D
29、ec-2001 / Jim ChristyCompany ConfidentialThe Difference Between SST and sLT ! meanTimeDimensionShort term Standard DeviationLong term Standard DeviationSubgroup size n = 5Number of subgroups N = 7TRENDSubgroup No. 125 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialThe differen
30、ce 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 deviation :Long-term standard deviation :The difference between sST and sLT26 NOKIA 2001 T0001801.PPT
31、/ 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 larger than sSTIf sLT equals sST, then the process control over the longer- term is the same as th
32、e 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. Alternatively sLT can be calculated
33、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 Data exercise 1.xls you find 100 measurements being the result of a capability study.
34、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. Mention possible causes of variation for parts.5.Calculate the sample mean and
35、 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-Dec-2001 / Jim ChristyCompany ConfidentialDefining Cp and PpSample meanPr
36、ocess 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 PpkSample meanProcess variation 3sProcess variation 3sMean - LSLUSL-MeanL
37、SL 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 Cpk Index accounts for process variability and centering of
38、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 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany Confiden
39、tialWhat 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 variation, i.e. a safety marginAre we able to improve o
40、ur 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 NOKIA
41、 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 deviation2 * standard deviation
42、2 * 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 = Cpk, If Pp
43、= 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 th
44、is case 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)Pp=Ppk=1,33 63 ppm defects = 0,006%Cp=Cpk=1,67 0,6
45、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 T0001801.PPT/ 21-Dec-20
46、01 / 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?39 NOKIA 2001
47、 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 - LSL6*
48、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 - L
49、SL6*sUSL - MeanMean - LSL3*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 Spreads
50、heet45 NOKIA 2001 T0001801.PPT/ 21-Dec-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 the
51、m 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 diamonds)6. Fill data into the NMP data collecti
52、on 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 shown46 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany Confiden
53、tialData Collection Sheet (DMM00024-EN-5.0)47 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialData Collection Sheet (DMM00024-EN-5.0)48 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialGraphical Presentation: HistogramWhat kind of distribution? Location ver
54、sus tolerance area Width (deviation)Example :Cp2.59 Pp1.86Cpk 0.88 Ppk 0.6349 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialGraphical Presentation: X-bar and R-ChartX-Bar ChartR-Chart50 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialGraphical Presentati
55、on - Time Series PlotSomething happened here !51 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialExercise 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
56、dimension 13.Analyse the remaining data sets an comment the process, should any actions be made? Remember to create and look at the charts.52 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialSection 5.Confidence of Cpk53 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany
57、ConfidentialConfidence 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 5% that Cpk is either lower o
58、r higher than this confidence interval.95% confidence intervalActual cpkCpk upper confidence limitCpk lower confidence limit54 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialConfidence of CpkSmall sample sizes gives wide confidence intervals55 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialCpk Confidence Limits with a sample size of 100 and a nominal Cpk of 1.67
