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1、Process Capability(Cp/Cpk/Pp/Ppk)Global Training Material,Creator: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 By
2、Comments1.021st Dec01Jim Christy&Sren LundsfrydApproved for Global UseNOTE All comments and improvements should be addressed to the creator of this document.,Contents,SectionHeading/DescriptionPage1Variation,Tolerances and Dimensional Control42Population,Sample and Normal Distribution153Cp and Cpk C
3、oncept284Use of the NMP Data Collection Spreadsheet445Confidence of Cpk52,Process Capability-Evaluating Manufacturing Variation,AcknowledgementsBenny Matthiassen(NMP CMT,Copenhagen,Denmark)Frank Adler(NMP Alliance,Dallas,USA)Joni Laakso(NMP R&D,Salo,Finland)Jim Christy(NMP SRC,Southwood,UK),Section
4、1Variation,Tolerances and Dimensional Control,Two Types of Product Characteristics,Variable:A characteristic measured in physical units,e.g.millimetres,volts,amps,decibel and seconds.,In this training we deal with variables only,The Sources of Process/System Variation,Process,Two Types of Processes,
5、All processes have: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 causes,Unnatural variability=due to special causes,Shewhart(1
6、931),The Two Causes of Variation,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
7、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),Defect,USL,LSL,nominal value,Tolerances,LSL(lower specification limit)10,7,USL(upper specification limit)10,9,Acceptable part,Rejecte
8、d Part,Rejected Product,Nominal10,80,1,Rejected Part,A tolerance is a allowed maximum variation of a dimension.,Measurement Report,In most cases we measure only one part per cavity for measurement report,Example of Capability Analysis Data,For some critical dimensions we need to measure more than 1
9、partFor 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),Process Capability-What is it?,Process Capability is a measure of the inherent capability of a manufacturing process to be able to
10、 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.Process Performance
11、 includes special causes of variation not present in Process Capability,Process Performance is designated Pp and Ppk,Why Make Process Capability Studies,A process capability study would reveal that the tool should not be accepted,When a dimension needs to be kept properly within spec,we must study t
12、he process capability.but still this is no guarantee for the actual performance of the process as it is only an initial capability study,The Nokia Process Verification Process,Section 2.Population,Sample and Normal Distribution,The Bell Shaped(Normal)Distribution,Symmetrical shape with a peak in the
13、 middle of the range of the data.Indicates that the input variables(Xs)to the process are randomly influenced.,“Population Parameters”=Population mean=Population standard deviation,Population versus Sample,PopulationAn entire group of objects that have been made or will be made containing a characte
14、ristic of interest,SampleThe group of objects actually measured in a statistical studyA sample is usually a subset of the population of interest,The Normal Distribution,What Measurements Can Be Used to Describe a Process or System?,mean(average)or describes the location of the distribution,(m),a mea
15、sure 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):,The most simple measure of variability is the range.The range of a sample is defined by as the difference between the large
16、st 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 Process variation?,sST-often notated as or sigma,is another measure of dispersion or variability and stands for“short-term standard deviation”
17、,which measures the variability of a process or system using“rational”sub-grouping.,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),What Measurements Can Be Used to Describe Process variation?,d2*valu
18、es for SST,Example:,What Measurements Can Be Used to Describe Process variation?,The Difference Between SST and sLT!,The 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
19、(SPC).,Short-term standard deviation:,Long-term standard deviation:,The difference between sST and sLT,The difference between sST and sLT,The 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
20、 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 data is taken over a longer p
21、eriod of time.Alternatively sLT can be calculated on several occasions separated by time and the results compared to see whether sLT is stable,Exercise 1:Sample Distributions,1.In Excel file Data exercise 1.xls you find 100 measurements being the result of a capability study.The specification for th
22、e 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 sample standard deviation for
23、 the 100 measurements.Use the average and stdev functions Excel.,Section 3.Cp and Cpk Concept,Defining Cp and Pp,The tolerance area divided by the total process variation,irrespective of process centring.,Defining Cpk and Ppk,Cpk and Ppk Indexes account also for process centring.,What is the Differe
24、nce Between Cp and Cpk?,The Cp index only accounts for process variabilityThe Cpk Index accounts for process variability and centering of the process mean to the design nominal Therefore,Cp CpkNOTE:Same applies also for Pp and Ppk,What Do These Indexes Tell Us?,Simple numerical values to describe th
25、e quality of the process The higher the number the better,Requirement 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 margin,Are we able to improve our process by using SPC?,If index is low,following things should be give
26、n 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),Cpk-With a 2-sigma safety margin,Requirement for Cp and Cpk is 1.67 min.1.67
27、is a ratio of=5/3 or 10/6.,2*standard deviation,2*standard deviation,Cpk 1.67 the process NOT CAPABLE,Acceptability of Cpk Index,Cpk=1.67 the process is CAPABLE,Cpk=2.0 the process has reached Six Sigma level,What Do These Indexes Tell Us?,If Cp=Cpk,If Pp=Ppk,If Cpk Cp,If Ppk Pp,If Cp=Pp,If Cpk=Ppk,
28、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 this case,then process perfectly centred,then process not cent
29、red(check process mean against design nominal),Cp 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 ppm defects=0,00006%,Note:Ppm reject rates calculated from Cp&Cpk are based on the short term variation which may not represent the l
30、ong term reject rate,The Effects of Cpk and Cp on FFR,Exercise 2:Cp and Cpk,Calculate 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,whi
31、ch?,Estimate Cp and Cpk?,The width of the normal distributions shown include 3*s,Estimate Cp and Cpk?-A),LSL,USL,A),Mean and nominal,USL-LSL,6*s,USL-Mean,Mean-LSL,3*s,Estimate Cp and Cpk?-B),LSL,USL,B),Nominal,Mean,USL-LSL,6*s,USL-Mean,Mean-LSL,3*s,Estimate Cp and Cpk?-C),LSL,USL,C),Nominal,Mean,USL
32、-LSL,6*s,USL-Mean,Mean-LSL,3*s,Estimate Cp and Cpk?-D,USL,LSL,D),Nominal,Mean,USL-LSL,6*s,USL-Mean,Mean-LSL,3*s,Section 4.Use of the NMP Data Collection Spreadsheet,Example of how to Collect Data,1.Run in and stabilise process2.Note the main parameters for reference3.When the process is stable run t
33、he tool for 10 hours3.Take 5 parts out from each cavity every half hour and 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 fu
34、nctional characteristics(white diamonds)6.Fill data into the NMP data collection spreadsheet7.Analyse!,See DMY 00019-ENClassification and Marking of Functional Characteristics,Data Collection Sheet(DMM00024-EN-5.0),Data Collection Sheet(DMM00024-EN-5.0),Graphical Presentation:Histogram,What kind of
35、distribution?Location versus tolerance area Width(deviation)Example:Cp2.59Pp1.86Cpk0.88Ppk0.63,Graphical Presentation:X-bar and R-Chart,X-Bar Chart,R-Chart,Graphical Presentation-Time Series Plot,Exercise 3:Cpk Data Spreadsheet,Open spreadsheet Data exercice 3.xls.Dim 13 is identical to the data fro
36、m the previous 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.,Section 5.Confidence of Cpk,Confidence of Cpk,Cpk values are not definite numbers as t
37、hey 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 or higher than this confidence interval.,Confidence of Cpk,Small sample sizes gives wide confidence intervals,Cpk Confidence Limits with a sample size of 100 and a nominal Cpk of 1.67,
