过程能力.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,2020/8/9 Sunday,#,2026/11/12,过程能力,Contents,SectionHeading/DescriptionPage,1,Variation,Tolerances and Dimensional Control4,2Population,Sample and Normal Distribution15,3Cp and Cpk Concept28,4Use of the NMP Data Collection Spreadsheet44,5Confidence of Cpk52,Process Capability,-Evaluating Manufacturing Variation,Acknowledgements,Benny 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 1,Variation,Tolerances and Dimensional Control,Two Types of Product Characteristics,Variable,:A characteristic measured in physical units,e.g.millimetres,volts,amps,decibel and seconds.,ON,OFF,Attribute,: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 only,The Sources of Process/System Variation,Methods,Operators,Customer Satisfaction,Material,Environment,Equipment,Process,Two Types of Processes,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,USL,LSL,nominal value,Defect,USL,LSL,nominal value,Unnatural variability,=due to special causes,Shewhart(1931),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 process,Identifying 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 circumstances,Special causes can be identified using Statistical Process Control(SPC),USL,LSL,Nominalvalue,Defect,USL,LSL,nominal value,Tolerances,LSL(lower specification limit),10,7,USL(upper specification limit),10,9,Acceptable part,Rejected Part,Rejected Product,Nominal,10,8,0,1,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 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 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 consistently produce components that meet the required design specifications,Process Capability is designated by,C,p,and,C,pk,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,P,p,and,P,pk,Why Make Process Capability Studies,LSL(lower specification limit),10,7,USL(upper specification limit),10,9,Nominal,10,8,0,1,This part is within spec.The tool would be approved if only this part was measured,These parts are out of spec and could be approved if only one good part was measured,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 the process capability,.but still this is no guarantee for the actual performance of the process as it is only an initial capability study,E1.5,E1,E2,E3,E4,E5,The Nokia Process Verification Process,Black diamonds to be fixed by E3(often a change of a white diamond),Proposal for black diamonds to be discussed with Supplier.,Max:105,85,Ongoing Process Control(SPC),Tolerances applied to drawing,Type 1 Functional Characteristics,-1 part/cavity measured for measurement report,White diamonds(s)to be agreed,White diamonds(s)to be discussed with supplier,10 parts/cavity measured for measurement report,Capability 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),Section 2.,Population,Sample and Normal Distribution,The Bell Shaped(Normal)Distribution,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.,“Population Parameters”,=Population mean,=Population standard deviation,Population versus Sample,Population,An entire group of objects that have been made or will be made containing a characteristic of interest,Sample,The group of objects actually measured in a statistical study,A sample is usually a subset of the population of interest,Population,Sample,“Sample Statistics”,x=Sample mean,s=Sample standard deviation,The Normal Distribution,What Measurements Can Be Used to Describe a Process or System?,Example:,1,=5,2,=7,3,=4,4,=2,5,=6,mean,(average)or describes,the location,of the distribution,(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):,Example:,1,=5,2,=7,3,=4,4,=2,5,=6,The 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 Process variation?,s,ST,-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.,where,is the,range,of subgroup,j,N,the number of subgroups,and,d,2,*,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?,d,2,*,values for S,ST,Where:N=no.of sub-groups,n=no.of samples in each sub-group,d,2,*,d,2,Typical:N=20&n=5,x,3,x,2,x,1,x,10,x,_,t,Example:,What Measurements Can Be Used to Describe Process variation?,The Difference Between S,ST,and,s,LT,!,mean,Time,Dimension,Short term,Standard Deviation,Long term,Standard Deviation,Subgroup size n=5,Number of subgroups N=7,TREND,Subgroup No.1,The difference between the standard deviations,s,LT,and,s,ST,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 s,ST,and,s,LT,The difference between s,ST,and,s,LT,The difference between,s,LT,and,s,ST,is,only,in the way that the standard deviation is calculated,s,LT,is always the same or larger than,s,ST,If,s,LT,equals,s,ST,then the process control over the longer-term is the same as the short-term,and the process would,not,benefit from SPC,If,s,LT,is larger than,s,ST,then the process has lost control over the longer-term,and the process would benefit from SPC,The reliability of,s,LT,is improved if the data is taken over a longer period of time.Alternatively,s,LT,can be calculated on several occasions separated by time and the results compared to see whether,s,LT,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 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 sample standard deviation for the 100 measurements.Use the,average,and stdev functions Excel.,Section 3.,Cp and Cpk Concept,Defining Cp and Pp,Sample mean,Process variation,6*,s,USL-LSL,LSL,USL,Nominal dim,The tolerance area divided by the total process variation,irrespective of process centring.,Defining Cpk and Ppk,Sample mean,Process variation,3,s,Process variation,3,s,Mean,-LSL,USL,-Mean,LSL,USL,Nominal dim,C,pk,and P,pk,Indexes account also for process centring.,What is the Difference Between Cp and Cpk?,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 Ppk,Cp=Cpk,(both low),LSL,USL,Mean=,Nominal,Reject parts,Reject parts,Cp high,Cpk low,Process should be optimized!,Nominal,LSL,Mean,USL,Reject parts,What Do These Indexes Tell Us?,Simple numerical values to describe the quality of the process,The higher the number the better,Requirement for C,p,and C,pk,is,1.67 min.,Recommendation for P,p,and P,pk,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 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),C,pk,-With a 2-sigma safety margin,-3 s,ST,+3 s,ST,LCL,UCL,LSL,USL,Mean value,=Nominal value or Target,Requirement for,C,p,and,C,pk,is,1.67 min.,1.67 is a ratio of=5/3 or 10/6.,6*standard deviation,10*standard deviation,2*standard deviation,2*standard deviation,C,pk,=1.67,the process is,CAPABLE,C,pk,=2.0,the process has reached,Six Sigma,level,What Do These Indexes Tell Us?,If C,p,=C,pk,If P,p,=P,pk,If C,pk,C,p,If P,pk,P,p,If C,p,=P,p,If C,pk,=P,pk,If P,p,C,p,If P,pk,C,pk,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 centred,(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 long 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.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?,Estimate Cp and Cpk?,The width of the normal distributions shown include 3*s,LSL,USL,A),LSL,USL,B),LSL,USL,C),USL,LSL,D),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-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 process,2.Note the main parameters for reference,3.When the process is stable run the tool for 10 hours,3.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 reference,5.Measure and record the main functional characteristics(white diamonds),6.Fill data into the NMP data collection spreadsheet,7.Analyse!,See DMY 00019-EN,Classification and Marking of Functional Characteristics,Time,Dimension,Subgroup size n=5,Number of subgroups N=20,0,5 hours between samples taken,Note:For clarity,only 6 subgroups are shown,Data Collection Sheet(DMM00024-EN-5.0),Data Collection Sheet(DMM00024-EN-5.0),Graphical Presentation:Histogram,What kind of distribution?,Location versus tolerance area,Width(deviation),Example:C,p,2.59P,p,1.86,C,pk,0.88P,pk,0.63,Graphical Presentation:X-bar and R-Chart,X-Bar Chart,R-Chart,Graphical Presentation-Time Series Plot,Something happened here!,Exercise 3:Cpk Data Spreadsheet,Open spreadsheet,Data exercice 3.xls,.Dim 13 is identical to the data from 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 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 or higher than this confidence interval.,95%confidence interval,Actual cpk,Cpk upper confidence limit,Cpk lower confidence limit,Confidence of Cpk,Small sample sizes gives wide confidence intervals,