1、Company 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 :IssueDateHandled ByComments1.021st D
2、ec01Jim Christy & Sren LundsfrydApproved for Global UseNOTE All comments and improvements should be addressed to the creator of this document.Company ConfidentialSectionHeading / DescriptionPage1Variation, Tolerances and Dimensional Control42Population, Sample and Normal Distribution153Cp and Cpk Co
3、ncept284Use of the NMP Data Collection Spreadsheet445Confidence of Cpk52Company ConfidentialAcknowledgementsBenny Matthiassen(NMP CMT, Copenhagen, Denmark)Frank Adler(NMP Alliance, Dallas, USA)Joni Laakso(NMP R&D, Salo, Finland)Jim Christy(NMP SRC, Southwood, UK)Company ConfidentialVariation, Tolera
4、nces and Dimensional ControlCompany ConfidentialVariable: 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 scratches (visual quality).In this
5、training we deal with variables onlyCompany ConfidentialMethodsOperatorsCustomer SatisfactionMaterialEnvironmentEquipmentProcessCompany Confidential All processes have: Natural (random) variability= due to common causes Stable Process:A process in which variation in outcomes arises only from common
6、causes Unstable Process: A process in which variation is a result of both common and special causesUSLLSLnominal valueDefectUSLLSLnominal value Unnatural variability= due to special causesCompany Confidential Common Causes: Causes that are implemented in the process due to the design of the process,
7、 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 circumstancesSpecial causes can be
8、identified using Statistical Process Control (SPC)USLLSLNominalvalueDefectUSLLSLnominal valueCompany ConfidentialLSL (lower specification limit)10,7USL (upper specification limit)10,9Acceptable partRejected PartRejected ProductNominal10,80,1Rejected PartA tolerance is a allowed maximum variation of
9、a dimension.Company ConfidentialIn most cases we measure only one part per cavity for measurement reportCompany Confidential 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 b
10、asis of production quantity, run duration and cycle time)1st Subgroup2nd Subgroup3rd Subgroup4th Subgroup118.53118.52118.54118.56118.54118.54118.52118.55118.51118.51118.50118.55118.53118.51118.52118.55118.51118.54118.54118.555th Subgroup6th Subgroup7th Subgroup8th Subgroup118.55118.54118.57118.60118
11、.54118.56118.56118.57118.55118.55118.57118.55118.54118.54118.55118.56118.56118.53118.54118.559th Subgroup10th Subgroup 11th Subgroup 12th Subgroup118.60118.61118.58118.60118.59118.60118.60118.63118.58118.61118.61118.63118.60118.59118.60118.61118.59118.59118.59118.64Company Confidential Process Capab
12、ility is a measure of the inherent capability of a manufacturing process 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 consistent
13、ly produce components that meet the required design specifications. Process Performance includes special causes of variation not present in Process Capability Process Performance is designated Pp and PpkCompany ConfidentialLSL (lower specification limit)10,7USL (upper specification limit)10,9Nominal
14、10,80,1This 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 good part was measuredA process capability study would reveal that the tool should not be acceptedWhen a dimension needs to be kept properly within
15、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 studyCompany Confidential E1.5 E1 E2 E3 E4 E5Black diamonds to be fixed by E3 (often a change of a white diamond)Proposal for black diamonds to be
16、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 measurement reportCa
17、pability 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)Company ConfidentialCompany Confidential Symmetrical shape
18、with a peak in the middle of the range of the data. Indicates that the input variables (Xs) to the process are randomly influenced. Company Confidential“Population Parameters” = Population mean = Population standard deviationPopulation An entire group of objects that have been made or will be made c
19、ontaining a characteristic of interestSample The group of objects actually measured in a statistical study A sample is usually a subset of the population of interestPopulationSample“Sample Statistics”x = Sample means = Sample standard deviationCompany ConfidentialCompany ConfidentialxxxxNN12.Example
20、: x1 = 5x2 = 7x3 = 4x4 = 2x5 = 68.4524562475x mean (average) or 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) :x
21、Company Confidential),.,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 sam
22、ples in a sub-group, e.g. 5 consecutive parts from the manufacturing process. Company 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” su
23、b-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)RXXjjjmaxminCompany ConfidentialWhere: N = no. of sub-groups, n = no. of samples in each sub-groupTypical: N=20 & n=5Compa
24、ny Confidential 1)(.)()(222212NxxxxxxssNLTLT92.17 .315)8 .46()8 .42()8 .44()8 .47()8 .45(22222LTsExample:Company ConfidentialmeanTimeDimensionShort term Standard DeviationLong term Standard DeviationSubgroup size n = 5Number of subgroups N = 7TRENDSubgroup No. 1Company ConfidentialThe difference bet
25、ween 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).sxxxxxxNLTN()(). ()122221sRNdRdS TjjN122*Short-term standard deviation :Long-term standard deviationCompany ConfidentialThe dif
26、ference 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 the short-term, and the process would not benefit from SPCIf sLT is larger than sST, then
27、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 on several occasions separated by time and the results compared to see whether sLT is st
28、ableCompany Confidential1. 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. How well does the sample population fit the specification, e.g. should we expect any parts outside spec?3. Mention possib
29、le 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 the average and stdev functions Excel.Company ConfidentialCompany ConfidentialSample meanProcess variation 6*sstpsL
30、SLUSLC*6- USL-LSLLSL USLNominal dimltpsLSLUSLP*6-The tolerance area divided by the total process variation, irrespective of process centring.Company ConfidentialststpksmeanUSLsLSLmeanC*3-,*3-minSample meanProcess variation 3sProcess variation 3sMean - LSLUSL-MeanLSL USLNominal dimltltpksmeanUSLsLSLm
31、eanP*3-,*3-minCpk and Ppk Indexes account also for process centring.Company Confidential The Cp index only accounts for process variability The Cpk Index accounts for process variability and centering of the process mean to the design nominal Therefore, Cp Cpk NOTE: Same applies also for Pp and PpkC
32、p = Cpk (both low)LSLUSLMean = NominalReject partsReject partsCp high, Cpk low Process should be optimized!NominalLSLMeanUSLReject partsCompany ConfidentialSimple numerical values to describe the quality of the process The higher the number the betterRequirement for Cp and Cpk is 1.67 min.Recommenda
33、tion 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 correctly?Too tight?Is the process capable of
34、 producing good quality products? Process variation? DOE required?Is the measuring system capable? (See Gage R&R)Company 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 * standa
35、rd deviation2 * standard deviation2 * standard deviationCompany ConfidentialCpk = 1.67 the process is CAPABLECpk = 2.0 the process has reached Six Sigma levelCompany 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
36、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 nomi
37、nal)Company 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%0.254.8638.9331.0228.2527.5627.4427.4327.4327.4327.4327.4327.4327.4327.4327.4327.4327.4327.
38、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%0.513.368.477.036.736.696.686.686.686.686.686.686.686.686.686.686.68%0.67.194.413.733.613.593.593.593.593.593
39、.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%1.027001509136313501350135013501350135013501350PPM1.1967532485484483483483483483483PPM1.23181651601591591591
40、59159159PPM1.336338333332323232PPM1.427141313131313PPM1.5733333PPM1.670.60.30.30.30.3PPM2.00.00.00.00.0PPM2.50.00.00.0PPM3.00.00.0PPM4.00.0PPMPp=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 are based on the short term variation
41、 which may not represent the long term reject rate Company ConfidentialCpkCpPpm defectsTotal number of defects for 50,000,000 partsTotal number of defects if phone has 10 of these parts0.81.338,200410,0004,100,00011.331,35067,500675,0001.331.33633,15031,5001.331.67331,65016,5001.501.5073503,5001.671
42、.671303002.002.00001Company Confidential Calculate Cp and Cpk for the 100 measurements in the file Data exercise 1.xls Determine the approximate Cp and Cpk for the 4 sample populations on the following page Should actions be made to improve these processes. If yes, which?Company ConfidentialThe widt
43、h of the normal distributions shown include 3*sLSLUSLA)LSLUSLB)LSLUSLC)USLLSLD)Company ConfidentialLSLUSLA)Mean and nominalUSL - LSL6*sUSL - MeanMean - LSL3*sCompany ConfidentialLSLUSLB)NominalMeanUSL - LSL6*sUSL - MeanMean - LSL3*sCompany ConfidentialLSLUSLC)NominalMeanUSL - LSL6*sUSL - MeanMean -
44、LSL3*sCompany ConfidentialUSLLSLD)NominalMeanUSL - LSL6*sUSL - MeanMean - LSL3*sCompany ConfidentialCompany Confidential1.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 a
45、nd 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 diamonds)6.Fill data into the NMP data
46、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 shownCompany ConfidentialCompany ConfidentialCompany Confidential W
47、hat kind of distribution? Location versus tolerance area Width (deviation) Example :Cp2.59Pp1.86Cpk0.88Ppk0.63Company ConfidentialX-Bar ChartR-ChartCompany ConfidentialSomething happened here !Company Confidential Open spreadsheet Data exercice 3.xls. Dim 13 is identical to the data from the previou
48、s exercises. Verify the results from the previous exercises for dimension 13. Analyse the remaining data sets an comment the process, should any actions be made? Remember to create and look at the charts.Company ConfidentialCompany Confidential Cpk values are not definite numbers as they are based o
49、n 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 or higher than this confidence interval.95% confidence intervalActual cpkCpk upper confidence limitCpk lower confidence limitCompany Confidential95% Confidence Interval on a Cpk of 1.670.0000.5001.0001.5002.0002.5003.0003.500050100150200250Sample SizeCpkCpk.LCpk.USmall sample sizes gives wide confidence intervalsCompany Confidential
