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 DocMan
2、Change 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 / Jim ChristyCompany ConfidentialSectionHeading / DescriptionPage1V
3、ariation, 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 ConfidentialAcknowledgementsBenny Matthiassen(NMP CMT, Copenhage
4、n, 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 ConfidentialVariation, Tolerances and Dimensional Control5 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany Conf
5、identialVariable: 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 training we deal with variables only6 NO
6、KIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialMethodsOperatorsCustomer SatisfactionMaterialEnvironmentEquipmentProcess7 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany Confidential All processes have: Natural (random) variability= due to common causes Stable Process:A
7、 process in which variation in outcomes arises only from common causes 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 Chr
8、istyCompany Confidential Common 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 pr
9、ocess all the time 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 ConfidentialLSL (lower specific
10、ation limit)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 ConfidentialIn most cases we measure only one part per cavi
11、ty for measurement report11 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany 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 basis of production quantit
12、y, 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 Subgroup118.55118.54118.57118.60118.54118.56118.56118.57118.5
13、5118.55118.57118.55118.54118.54118.55118.56118.56118.53118.54118.559th Subgroup10th Subgroup 11th Subgroup 12th Subgroup118.60118.61118.58118.60118.59118.60118.60118.63118.58118.61118.61118.63118.60118.59118.60118.61118.59118.59118.59118.6412 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany
14、 Confidential 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 specifications Process Capability is designated by Cp and Cpk Process Performance is a measure of the performance of a proce
15、ss to be able to consistently 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 Ppk13 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany Confident
16、ialLSL (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 good part was measuredA process capability study would reveal that t
17、he 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 study14 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany C
18、onfidential 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 discussed with Supplier.Max: 105,85Ongoing Process Control (SPC) Tolerances applied to drawingType 1 Functional Characteristics- 1 part/cavity measured for measurement
19、 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 cavity = 100 parts.
20、 Can vary depending on tool capacity, e.g. stamped parts (see DMY00019-EN)15 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany 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
21、 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 An entire group of objects that have been made or will be made containin
22、g 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 deviation18 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany Con
23、fidential19 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialxxxxNN12.Example: 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. Wh
24、en 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 Confidential),.,min(),.,max(2121NNxxxxxxRExample: x1 = 5x2 = 7x3 = 4x4 = 2x5 = 6527)6 , 2 , 4 , 7 , 5min()6 , 2 , 4 , 7 , 5max(RThe most simp
25、le 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. 21 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany Confidenti
26、alsST - 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.sRNdRdS TjjN122*where is the range of subgroup j, N the number of subgroups, and d2*
27、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 each sub-groupTypical: N=20 & n=523 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim Ch
28、ristyCompany 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 DeviationLong term Standard DeviationSubgroup size n = 5Number of subgroups
29、 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 control, like Statistical Process Control (SPC).sxxxxxxNLTN
30、()(). ()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 calculatedsLT is always the same or larger than sSTIf
31、 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 improved if the
32、 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 file Data exercise 1.xls you find 100 meas
33、urements 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. Mention possible causes of v
34、ariation 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 ChristyCompany ConfidentialSample me
35、anProcess 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 meanProcess variat
36、ion 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 Index accounts for
37、 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.PPT/ 21
38、-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 i
39、mprove 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)
40、33 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 N
41、OKIA 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 ConfidentialIf Cp = Cpk, If Pp = Ppk, If Cpk Cp, If Ppk Pp, If Cp = Pp, If Cpk = Ppk, If
42、 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 case then process perfectly centred then process not c
43、entred (check process mean against design nominal)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.
44、2138.21%0.254.8638.9331.0228.2527.5627.4427.4327.4327.4327.4327.4327.4327.4327.4327.4327.4327.4327.4327.43%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.
45、477.036.736.696.686.686.686.686.686.686.686.686.686.686.68%0.67.194.413.733.613.593.593.593.593.593.593.593.593.593.593.59%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%1.0270015
46、09136313501350135013501350135013501350PPM1.1967532485484483483483483483483PPM1.2318165160159159159159159159PPM1.336338333332323232PPM1.427141313131313PPM1.5733333PPM1.670.60.30.30.30.3PPM2.00.00.00.00.0PPM2.50.00.00.0PPM3.00.00.0PPM4.00.0PPMPp=Ppk=1,33 63 ppm defects = 0,006%Cp=Cpk=1,67 0,6 ppm defe
47、cts = 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 ConfidentialCpkCpPpm defectsTotal number of defects for 50,000,000 partsTotal number of d
48、efects if phone has 10 of these parts0.81.338,200410,0004,100,00011.331,35067,500675,0001.331.33633,15031,5001.331.67331,65016,5001.501.5073503,5001.671.671303002.002.0000138 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany Confidential Calculate Cp and Cpk for the 100 measurements in the f
49、ile 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?39 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / Jim ChristyCompany ConfidentialThe width of the normal distributions shown includ
50、e 3*sLSLUSLA)LSLUSLB)LSLUSLC)USLLSLD)40 NOKIA 2001 T0001801.PPT/ 21-Dec-2001 / 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 N
