6s黑带培训教材1英文

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Process Capability Analysis,72,Process Capability Analysis,(,Measure Phase),Scope of Module,Process Variation,Process Capability,Specification, Process and Control Limits,Process Potential vs Process Performance,Short-Term vs Long-Term Process Capability,Process Capability for Non-Normal Data,Cycle-Time(Exponential Distribution),Reject Rate(Binomial Distribution),Defect Rate(Poisson Distribution),Process Variation,Process Variation,is the inevitable differences among individual,measurements or units produced by a process.,Sources of Variation,within unit(positional variation),between units(unit-unit variation),between lots(lot-lot variation),between lines(line-line variation),across time(time-time variation),measurement error(repeatability & reproducibility),Types of Variation,Inherent or Natural Variation,Due to the cumulative effect of many small unavoidable causes,A process operating with only chance causes of variation present is said to be “in statistical control”,Types of Variation,Special or Assignable Variation,May be due to a) improperly adjusted machine,b) operator error,c) defective raw material,A process operating in the presence of assignable causes of variation is said to be “out-of-control”,Process Capability,Process Capability,is the inherent reproducibility of a processs,output. It measures how well the process is currently behaving,with respect to the output specifications. It refers to the uniformity,of the process.,Capability is often thought of in terms of the proportion of output,that will be within product specification tolerances. The frequency,of defectives produced may be measured in,a)percentage (%),b)parts per million (ppm),c)parts per billion (ppb),Process Capability,Process Capability,studies can,indicate the consistency of the process output,indicate the degree to which the output meets specifications,be used for comparison with another process or competitor,Process Capability vs Specification Limits,a),b),c),a) Process is highly capable,b) Process is marginally capable,c) Process is not capable,Three Types of Limits,Specification Limits (LSL and USL),created by design engineering in response to customer requirements to specify the tolerance for a products characteristic,Process Limits (LPL and UPL),measures the variation of a process,the natural 6, limits of the measured characteristic,Control Limits (LCL and UCL),measures the variation of a sample statistic (mean, variance, proportion, etc),Three Types of Limits,Distribution of Individual Values,Distribution of Sample Averages,Process Capability Indices,Two measures of process capability,Process Potential,C,p,Process Performance,C,pu,C,pl,C,pk,Process Potential,The C,p,index assesses whether the natural tolerance (6,) of a,process is within the specification limits.,Process Potential,A C,p,of 1.0 indicates that a process is judged to be “capable”,i.e. if the process is centered within its engineering tolerance,0.27% of parts produced will be beyond specification limits.,C,p,Reject Rate,1.000.270 %,1.330.007 %,1.506.8 ppm,2.002.0 ppb,Process Potential,a),b),c),a) Process is highly capable (C,p,2),b) Process is capable (C,p,=1 to 2),c) Process is not capable (C,p,1.5),b) Process is capable (C,pk,=1 to 1.5),c) Process is not capable (C,pk,1),a),C,p,= 2,C,pk,= 2,b),C,p,= 2,C,pk,= 1,c),C,p,= 2,C,pk, 1,Example 1,Specification Limits:4 to 16 g,MachineMeanStd Dev,(a) 10 4,(b) 10 2,(c) 7 2,(d) 13 1,Determine the corresponding C,p,and C,pk,for each machine.,Example 1A,Example 1B,Example 1C,Example 1D,Process Capability,For a normally distributed characteristic, the defective rate,F(x),may be,estimated via the following:,For characteristics with only one specification limit:,a)LSL only,b)USL only,LSL,USL,Example 2,Specification Limits:4 to 16 g,MachineMeanStd Dev,(a) 10 4,(b) 10 2,(c) 7 2,(d) 13 1,Determine the defective rate for each machine.,Example 2,Mean Std Dev Z,LSL,Z,USL,F(xUSL) F(x),10 4 -1.51.5 66,807 66,807133,614,10 2 -3.03.0 1,350 1,350 2,700,7 2 -1.54.5 66,807 3 66,811,13 1 -9.03.0 0 1,350 1,350,Lower Spec Limit= 4 g,Upper Spec Limit= 16 g,Process Potential vs Process Performance,(,a) Poor Process Potential(b) Poor Process Performance,LSL,USL,LSL,USL,Experimental Design,to reduce variation,Experimental Design,to center mean,to reduce variation,Process Potential vs Process Performance,Process Potential Index (C,p,),C,pk,1.0 1.2 1.4 1.6 1.8 2.0,1.0,2,699.91,363.31,350.01,350.01,350.01,350.0,1.2,318.3 159.9 159.1 159.1 159.1,1.4,26.7 13.4 13.4 13.4,1.6,1.6 0.8 0.8,1.8,0.1 0.0,2.0,0.0,Defective Rate (measured in dppm) is dependent on the actual,combination of C,p,and C,pk,.,Process Potential vs Process Performance,a),C,p,= 2,C,pk,= 2,b),C,p,= 2,C,pk,= 1,c),C,p,= 2,C,pk, 1,C,p, C,pk,Missed Opportunity,Alternative Process Performance Index,Process capability statistics measure process variation relative to specification limits.,The C,p,statistic compares the engineering tolerance against the processs natural variation.,The C,pk,statistic takes into account the location of the process relative to the midpoint between specifications. If the process,target is not centered between specifications, the C,pm,statistic is preferred.,Process Stability,A process is stable if the distribution of measurements made,on the given feature is consistent over time.,Time,Stable Process,Time,Unstable Process,ucl,lcl,ucl,lcl,Within vs Overall Capability,Within Capability,(previously called,short-term capability,) shows the inherent variability of a machine/process operating within a brief period of time.,Overall Capability,(previously called,long-term capability,) shows the variability of a machine/process operating over a period of time. It includes sources of variation in addition to the short-term variability.,Within vs Overall Capability,WithinOverall,Sample Size30 50 units, 100 units,Number of Lotssingle lotseveral lots,Period of Timehours or daysweeks or months,Number of Operatorssingle operatordifferent operators,Process Potential C,p,P,p,Process Performance C,pk,P,pk,Within vs Overall Capability,Within CapabilityOverall Capability,The key difference between the two sets of indices lies in the estimates for,Within,and ,Overall,.,Estimating,Within,and ,Overall,Consider the following observations from a Control Chart:,S/NX,1,X,2, X,k,MeanRangeStd Dev,1x,1,1,x,2,1, x,k,1,X,1,R,1,S,1,2x,1,2,x,2,2, x,k,2,X,2,R,2,S,2,: : : : : : :,mx,1,m,x,2,m, x,k,m,X,m,R,m,S,m,The overall variation,Overall,is estimated by,Estimating,Within,and ,Overall,The within variation,Within,may be estimated by one of the following:,(a)R-bar Method,whered,2,is a Shewhart constant =,(k),(b)S-bar Method,wherec,4,is a Shewhart constant =,(k),(c)Pooled Standard Deviation Method,In MiniTab, the,Pooled Standard Deviation,is the default method.,Estimating,Within,and ,Overall,In cases where there is only 1 observation per sub-group (i.e. k=1),the,Moving Range Method,is used, where .,The,within variation,Within,is then estimated using either,a)the,Average Moving Range,:,b)the,Median Moving Range,:,Example 3,The length of a camshaft for an automobile engine is specified,at 600 2 mm. Control of the length of the camshaft is critical,to avoid scrap/rework.,The camshaft is provided by an external supplier. Assess the,process capability for this supplier.,The data is available in,Process Capability Analysis.MTW,.,Example 3,S,tat,Q,uality Tools Capability,A,nalysis (Normal),Example 3,Example 3A,Histogram of camshaft length suggests mixed populations.,Further investigation revealed that there are two suppliers for,the camshaft. Data was collected over camshafts from both,sources.,Are the two suppliers similar in performance?,If not, what are your recommendations?,Example 3A,S,tat,Q,uality Tools Capability,S,ixpack(Normal),Example 3A,Example 3A,Whats Six Sigma Quality Then,Original Definition by Motorola:,if the specification limits are at least 6, away from the process mean , i.e. C,p, 2,and the process shifts by less than 1.5, i.e. C,pk, 1.5,then the process will yield less than 3.4 dppm rejects.,6,6,Shift,1.5,4.5,Whats Six Sigma Quality Now,Mikel J Harry claims that the process mean between lots will vary, with an average process shift of,1.5.,k, =,z, + 1.5,k, =,z, + 1.5,Shift,1.5,z,Note:,Sigma Capability = (dpmo),(dppm),Process Capability for Non-Normal Data,Not every measured characteristic is normally distributed.,CharacteristicDistribution,Cycle TimeExponential,Reject RateBinomial,Defect RatePoisson,Process Capability for Cycle Time,The,Weibull Distribution,is a general family of distribution with,where,scale parameter, is the value at which CDF=68.17%,and,shape parameter, determines the shape of the PDF.,Process Capability for Cycle Time,At,=1,the,Weibull Distribution,is reduced to,For an,Exponential Distribution,The,Exponential Distribution,is thus a,Weibull Distribution,with =1.,Weibull (x;,=1, ),Exponential (x;,),Example 4,A customer service manager wants to determine the process,capability for his department. A primary performance index,is the time taken to close a customer complaint. The goal for,this index is to close a complaint within one calendar week.,Performance over the last 400 complaints was reviewed.,Example 4,S,tat,Q,uality Tools Capability,A,nalysis (Weibull),Example 4,Example 4A,S,tat,Q,uality Tools Capability Sixpack (Wei,b,ull),Example 4A,Process Capability for Reject Rate,For a,Normal Distribution, the proportion of parts produced beyond a,specification limit is,Reject Rate,Process Capability for Reject Rate,Thus, for every reject rate there is an accompanying Z-Score,where,Recall that,Hence,Process Capability for Reject Rate,Estimation of P,pk,for Reject Rate,Determine the long-term,reject rate,(,p,),Determine the,inverse cumulative probability,for,p,using,C,alc, Probability,D,istribution ,N,ormal,Z-Score,is the magnitude of the returned value,P,pk,is one-third of the,Z-Score,Example 5,A sales manager plans to assess the process capability of his,telephone sales departments handling of incoming calls.,The following data was collected over a period of 20 days:,number of incoming calls per day,number of unanswered calls per days,Example 5,S,tat,Q,uality Tools Capability Analysis (Bi,n,omial),Example 5,P,pk,= 0.25,Process Capability for Defect Rate,Other applications, approximating a,Poisson Distribution,:,error rates,particle count,chemical concentration,Process Capability for Defect Rate,Estimation of Y,tp,for Defect Rate,Define size of an inspection unit,Determine the long-term,defects per unit,(,DPU,),DPU= Total Defects, Total Units,Determine the,throughput yield,(,Y,tp,),Y,tp,= expDPU,Process Capability for Defect Rate,Estimation of Sigma-Capability for Defect Rate,Determine the,opportunities per unit,Determine the long-term,defects per opportunity,(,d,),d= defects per unit,opportunities per unit,Determine the,inverse cumulative probability,for,d,using,C,alc, Probability,D,istribution ,N,ormal,Z-Score,is the magnitude of the returned value,Sigma-Capability,=,Z-Score,+ 1.5,Example 6,The process manager for a wire manufacturer is concerned,about the effectiveness of the wire insulation process.,Random lengths of electrical wiring are taken and tested for,weak spots in their insulation by means of a test voltage.,The number of weak spots and the length of each piece of,wire are recorded.,Example 6,S,tat,Q,uality Tools Capability Analysis (Poiss,o,n),Example 6,Defects per Unit,= 0.0265194,Throughput Yield,= expDPU,= exp0.0265194,= 0.9738,c.f. First-Time Yield,= 2 / 100,= 0.02,Example 6,Define,1 Inspection Unit= 125 unit length of wire,i.e.,Units,=,Length, 125,Example 6A,S,tat,Q,uality Tools Capability Analysis (Poiss,o,n),Example 6A,Defects per Unit,= 3.31493,Throughput Yield,= expDPU,= exp3.31493,= 0.0363,c.f. First-Time Yield,= 2 / 100,= 0.02,Example 6B,Defects per Unit,= 3.31493,Opportunities per Unit,= 1,Defects per Opportunity,= 3.31493,Z-Score = ?,Example 6B,1,inspection unit,= 1 unit length of wire,Opportunities per Unit,= 1,Defects per Opportunity,= 329, 12,406,= 0.0265,Z-Score,= Abs,1,(0.0265),= 1.935,Sigma-Capability,= Z-Score + 1.5,= 3.435,DPU,Z-Score,Choice of Six Sigma Metric,