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1、2 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany ConfidentialSectionHeading / DescriptionPage1Variation, Tolerances and Dimensional Control42Population, Sample and Normal Distribution153Cp and Cpk Concept28Confidence Interval 3747Mini Cpk537 603 NOKIA 2005 T0001802.PPT/ 22-Feb-2005
2、/ Yrjo SaastamoinenCompany 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)4 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany Confidential5 NOKIA 200
3、5 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany 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 (visua
4、l quality).In this training we deal with variables only6 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany ConfidentialMethodsOperatorsCustomer SatisfactionMaterialEnvironmentEquipmentProcess7 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany Confidential All processes ha
5、ve: Natural (random) variability= due to common causes Stable Process:A 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 variabilit
6、y= due to special causes8 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany 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 o
7、f 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 identified using Statistical Process Control (SPC)USLLSLNominalvalueDefectUSLLSLnominal value9 NOKIA 2005
8、T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany ConfidentialLSL (lower specification 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 2005 T0001802.PPT/ 22-Feb-2
9、005 / Yrjo SaastamoinenCompany ConfidentialDim. NumberDim. 3Dim. 10Detailed descriptionLocationa3b2Measuring 18-Nov-0418-Nov-04Gauge I.D.CMMCMMTotal Gauge R&R (% Tolerance)7%3%Operator (Inspector)Type of dimension2Nom. Dim.1069,4Tolerance0,100,20Upper specification limit (USL)10,1069,60Lower specifi
10、cation limit (LSL)9,9069,20Dim. 3Dim. 10Part 110,0569,340Part 210,0369,370Part 310,169,410Part 410,0669,320Part 510,0869,310Mean check on 5 partsMean10,0669,35% tolerance64,0%-25,0%OK / NOT OK (+/-50%)Not OKOKRange check on 5 partsMax10,10069,410Min10,03069,310Range0,0700,100% tolerance interval35,0
11、%25,0%OK / NOT OK (Max = 30%)Not OKOKDiamond DimensionsAction plan. Required for each NotOK dim!Datum System / References usedMeasurement Device usedwhiteblackwhiteGO TO General Information SectionDim. NumberDim. 3Dim. 10Detailed descriptionsnap1Locationa3d2Measuring 18-Nov-0418-Nov-04Nom. Dim.1069,
12、4Tolerance0,100,20Upper specification limit (USL)10,1069,60Lower specification limit (LSL)9,9069,20Part 110,05069,250Mean check on 1 part% tolerance50,0%-75,0%OK / NOT OK (+/-50%)OKNot OKDim. 3Dim. 10Part 169,250Part 269,270Part 369,280Part 469,200Part 569,300Mean check on 5 partsMean69,26% toleranc
13、e-70,0%OK / NOT OK (+/-80%)OKRange check on 5 partsMax69,300Min69,200Range0,100% tolerance interval25,0%OK / NOT OK (Max = 30%)OKAction plan. Required for each NotOK dim!Datum System / References usedMeasurement Device usedBasic DimensionsGO TO General Information SectionFor Measurement report (FAI)
14、 we normally measure 1-5 parts per cavity depending on result and the type of the dimension11 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany 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 pc
15、s (but sampling plan needs to be made on the basis of production quantity, run duration and cycle time)1st Subgroup2nd Subgroup3rd Subgroup4th Subgroup118.53118.52118.54118.56118.54118.54118.52118.55118.51118.51118.50118.55118.53118.51118.52118.55118.51118.54118.54118.555th Subgroup6th Subgroup7th S
16、ubgroup8th Subgroup118.55118.54118.57118.60118.54118.56118.56118.57118.55118.55118.57118.55118.54118.54118.55118.56118.56118.53118.54118.559th Subgroup10th Subgroup 11th Subgroup 12th Subgroup118.60118.61118.58118.60118.59118.60118.60118.63118.58118.61118.61118.63118.60118.59118.60118.61118.59118.59
17、118.59118.6412 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany 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 designate
18、d 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. Process Performance includes special causes of variation not present in Process Capability Process Performance is designated Pp
19、 and Ppk13 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany ConfidentialLSL (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 appro
20、ved 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 process as it is only an in
21、itial capability study14 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany 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 discussed with Supplier.Max: 105,85Ongoing Process Control (SPC) Tolerances a
22、pplied to drawingType 1 Functional Characteristics- 1 part/cavity measured for measurement reportWhite diamonds(s) to be agreedWhite diamonds(s) to be discussed with supplier1-5 parts/cavity measured for measurement report(see DMY00019-EN) Capability study: Requirement: Cpk 1.67 and Ppk1.33 by E3.Qu
23、antities to be agreed with supplier. Eg. 5 parts every 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 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany Confidential16 NOKIA 2005 T0001802.PPT/ 22-Feb
24、-2005 / Yrjo SaastamoinenCompany 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 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany Confidential“Population Parameters” =
25、 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 population of interestPopulationSa
26、mple“Sample Statistics”x = Sample means = Sample standard deviation18 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany Confidential19 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany ConfidentialxxxxNN12.Example: x1 = 5x2 = 7x3 = 4x4 = 2x5 = 68.4524562475x mean (average
27、) 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) :x20 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo Saastamoinen
28、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
29、ples in a sub-group, e.g. 5 consecutive parts from the manufacturing process. 21 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany ConfidentialsST - often notated as or sigma, is another measure of dispersion or variability and stands for “short-term standard deviation”, which measures
30、 the variability of a process or system using “rational” sub-grouping.221dRdNRsNjjSTwhere is the range of subgroup j, N the number of subgroups, and d2 depends on the number of samples (n) within a subgroup (see next slide).minmaxjjXXRj22 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompa
31、ny Confidentialnd221.12831.69342.05952.32662.53472.70482.84792.970103.078113.173nd2223.819233.858243.895253.931263.965273.997284.028294.058n = no. of samples in each sub-groupnd2123.258133.336143.407153.472163.532173.588183.640193.689Typical: n=523 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo Saastam
32、oinenCompany Confidential 1)(.)()(222212NxxxxxxssNLTLT92.17 .315)8 .46()8 .42()8 .44()8 .47()8 .45(22222LTsExample:24 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany ConfidentialmeanTimeDimensionShort term Standard DeviationLong term Standard DeviationSubgroup size n = 5Number of sub
33、groups N = 7TRENDSubgroup No. 125 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany 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)
34、.sxxxxxxNLTN()(). ()122221sRNdRdS TjjN122*Short-term standard deviation :Long-term standard deviation26 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany ConfidentialThe difference between sLT and sST is only in the way that the standard deviation is calculatedsLT is always the same or
35、 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 SPCThe reliability of sLT
36、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 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany ConfidentialSample meanProcess variation 6
37、*sstpsLSLUSLC*6- USL-LSLLSL USLNominal dimltpsLSLUSLP*6-The tolerance area divided by the total process variation, irrespective of process centring.28 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany Confidential29 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany Confid
38、entialststpksmeanUSLsLSLmeanC*3-,*3-minSample meanProcess variation 3sProcess variation 3sMean - LSLUSL-MeanLSL USLNominal dimltltpksmeanUSLsLSLmeanP*3-,*3-minCpk and Ppk Indexes account also for process centring.30 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany Confidential The Cp
39、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 PpkCp = Cpk (both low)LSLUSLMean = NominalReject partsReject partsCp high, Cpk low Process should be
40、 optimized!NominalLSLMeanUSLReject parts31 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany 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
41、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?Is the process capable of producing good quality products? Process varia
42、tion? DOE required?Is the measuring system capable? (See Gage R&R)32 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany 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 deviatio
43、n10 * standard deviation2 * standard deviation2 * standard deviation33 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany ConfidentialCpk = 1.67 the process is CAPABLECpk = 2.0 the process has reached Six Sigma level34 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany Conf
44、identialIf Cp = Cpk, If Pp = Ppk, If Cpk Cp, If Ppk Pp, If Cp = Pp, If Cpk = Ppk, If Pp Cp, If Ppk 1,67Ppk1,33Corrective actionsNoStabilize Process & Visual QualityStep 1 -PreparationManufacture jigsGauge calibrationGauge R&RCollect and mark 5 consecutive parts every hrs until 20 sets have been crea
45、tedPrepare Cpk Spreadsheet for 100 partsStep 2 -Measure partsFill in measurement dataSend report and samples to NokiaSee charts page for warning points52 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany ConfidentialMeanCheck for Data (typing) ErrorNo ErrorErrorRange (or Variation)Chec
46、k last CalibrationNot OKEvaluate with Mechanical Design if Specification can be adjusted ?Check GR&R for this or similar dimensionOKOKNot OKBack to Step 3NoBack to Step 2 for that part/dimensionCheck Type of ErrorRe-CalibrateBack to Step 2Improve Measurement SystemBack to Step 2Modify Tool or Proces
47、sBack to Step 1Yes53 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany Confidential54 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany Confidential The Mini Cpk Study method follows the same principles of the Process Capability Study method of confidence intervals relati
48、ons to sample size. This means that a Cpk=1.67 for a sample size of 100 pcs is statistically equivalent to a Cpk =1.87 for a sample size of 40 pcs. The use of Mini Cpk study method may well reduce the measurement effort at the supplier and fasten the approval time. It is recommended to use the Mini
49、Cpk study method in the following cases: Pre-qualification of processes e.g before moving the tool to the final moulder location Re-qualification of processes after mass approval e.g when after major maintenance or colour change Copy tool approvals Regular tool approvals when agreed between the prog
50、ram and the supplier Note! For re-qualification (when the tool has not changed) measurements from only 1 cavity may be acceptable55 NOKIA 2005 T0001802.PPT/ 22-Feb-2005 / Yrjo SaastamoinenCompany Confidential Confidence Interval on Cpk / Ppk with N=100, lower CI on Ppk 1.33 is Ppk 1.14 if N=40, lowe