1、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)
2、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 lo
3、ts (lot-lot variation) between lines (line-line variation) across time (time-time variation) measurement error (repeatability & reproducibility),Types of Variation,Inherent or Natural VariationDue to the cumulative effect of many small unavoidable causes A process operating with only chance causes o
4、f variation present is said to be “in statistical control”,Types of Variation,Special or Assignable VariationMay be due to a) improperly adjusted machineb) operator errorc) defective raw material A process operating in the presence of assignable causes of variation is said to be “out-of-control”,Pro
5、cess 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 th
6、at 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 canindicate the consistency of the process outputindicate the degree to wh
7、ich the output meets specificationsbe 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
8、 design engineering in response to customer requirements to specify the tolerance for a products characteristicProcess Limits (LPL and UPL) measures the variation of a process the natural 6 limits of the measured characteristicControl Limits (LCL and UCL) measures the variation of a sample statistic
9、 (mean, variance, proportion, etc),Three Types of Limits,Distribution of Individual ValuesDistribution of Sample Averages,Process Capability Indices,Two measures of process capabilityProcess Potential Cp Process Performance Cpu Cpl Cpk,Process Potential,The Cp index assesses whether the natural tole
10、rance (6) of a process is within the specification limits.,Process Potential,A Cp 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.Cp Reject Rate1.00 0.270 %1.33 0.
11、007 %1.50 6.8 ppm2.00 2.0 ppb,Process Potential,a),b),c),a) Process is highly capable (Cp2) b) Process is capable (Cp=1 to 2) c) Process is not capable (Cp1),Process Potential,The Cp index compares the allowable spread (USL-LSL) against the process spread (6). It fails to take into account if the pr
12、ocess is not centered between the specification limits.,Process is centered,Process is not centered,Process Performance,The Cpk index relates the scaled distance between the process mean and the nearest specification limit.,Process Performance,Cpk Reject Rate1.0 0.13 0.27 %1.1 0.05 0.10 %1.2 0.02 0.
13、03 % 1.3 48.1 96.2 ppm1.4 13.4 26.7 ppm1.5 3.4 6.8 ppm1.6 794 1589 ppb1.7 170 340 ppb1.8 33 67 ppb1.9 6 12 ppb2.0 1 2 ppb,Process Performance,a) Process is highly capable (Cpk1.5) b) Process is capable (Cpk=1 to 1.5) c) Process is not capable (Cpk1),Example 1,Specification Limits : 4 to 16 gMachine
14、Mean Std Dev(a) 10 4(b) 10 2(c) 7 2(d) 13 1Determine the corresponding Cp and Cpk 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 s
15、pecification limit: a) LSL only b) USL only,LSL,USL,Example 2,Specification Limits : 4 to 16 gMachine Mean Std Dev(a) 10 4(b) 10 2(c) 7 2(d) 13 1Determine the defective rate for each machine.,Example 2,Mean Std Dev ZLSL ZUSL F(xUSL) F(x) 10 4 -1.5 1.5 66,807 66,807 133,614 10 2 -3.0 3.0 1,350 1,350
16、2,700 7 2 -1.5 4.5 66,807 3 66,811 13 1 -9.0 3.0 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,Experimental Designto reduce variation,Experimental Designto center meanto reduce variation,P
17、rocess Potential vs Process Performance,Process Potential Index (Cp)Cpk 1.0 1.2 1.4 1.6 1.8 2.01.0 2,699.9 1,363.3 1,350.0 1,350.0 1,350.0 1,350.0 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 actua
18、l combination of Cp and Cpk,Process Potential vs Process Performance,Cp Cpk Missed Opportunity,Alternative Process Performance Index,Process capability statistics measure process variation relative to specification limits. The Cp statistic compares the engineering tolerance against the processs natu
19、ral variation.The Cpk 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 Cpm statistic is preferred.,Process Stability,A process is stable if the distribution of measurements made
20、 on the given feature is consistent over time.,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 va
21、riability 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,Within OverallSample Size 30 50 units 100 unitsNumber of Lots single lot several lotsPeriod of Time hours or days weeks or monthsNu
22、mber of Operators single operator different operatorsProcess Potential Cp Pp Process Performance Cpk Ppk,Within vs Overall Capability,Within Capability Overall CapabilityThe key difference between the two sets of indices lies in the estimates for Within and Overall .,Estimating Within and Overall,Co
23、nsider the following observations from a Control Chart:S/N X1 X2 Xk Mean Range Std Dev1 x1,1 x2,1 xk,1 X1 R1 S12 x1,2 x2,2 xk,2 X2 R2 S2: : : : : : :m x1,m x2,m xk,m Xm Rm SmThe overall variation Overall is estimated by,Estimating Within and Overall,The within variation Within may be estimated by on
24、e of the following: (a) R-bar Methodwhere d2 is a Shewhart constant = (k)(b) S-bar Methodwhere c4 is a Shewhart constant = (k)(c) Pooled Standard Deviation MethodIn MiniTab, the Pooled Standard Deviation is the default method.,Estimating Within and Overall,In cases where there is only 1 observation
25、per sub-group (i.e. k=1), the Moving Range Method is used, where .The within variation Within is then estimated using eithera) 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 cam
26、shaft 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,Stat Quality Tools Capability Analysis (Normal),Example 3,Example 3A,Histogram of camshaft len
27、gth 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,Stat Quality Tools Capability Sixpack(Norm
28、al),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. Cp 2, and the process shifts by less than 1.5, i.e. Cpk 1.5, then the process will yield less than 3.4 dppm rejects.,Shift 1.5,Whats Si
29、x Sigma Quality Now,Mikel J Harry claims that the process mean between lots will vary, with an average process shift of 1.5.,Shift 1.5,Note: Sigma Capability = (dpmo) (dppm),Process Capability for Non-Normal Data,Not every measured characteristic is normally distributed.Characteristic DistributionCy
30、cle Time Exponential Reject Rate BinomialDefect Rate Poisson,Process Capability for Cycle Time,The Weibull Distribution is a general family of distribution withwhere scale parameter is the value at which CDF=68.17%, and shape parameter determines the shape of the PDF.,Process Capability for Cycle Ti
31、me,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 perfo
32、rmance 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,Stat Quality Tools Capability Analysis (Weibull),Example 4,Example 4A,Stat Quality Tools Capability
33、Sixpack (Weibull),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, whereRecall thatHence,Process Capab
34、ility for Reject Rate,Estimation of Ppk for Reject RateDetermine the long-term reject rate (p)Determine the inverse cumulative probability for p,using Calc Probability Distribution NormalZ-Score is the magnitude of the returned valuePpk is one-third of the Z-Score,Example 5,A sales manager plans to
35、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,Stat Quality Tools Capability Analysis (Binomial),Example 5,Process C
36、apability for Defect Rate,Other applications, approximating a Poisson Distribution :error ratesparticle countchemical concentration,Process Capability for Defect Rate,Estimation of Ytp for Defect RateDefine size of an inspection unitDetermine the long-term defects per unit (DPU)DPU = Total Defects T
37、otal UnitsDetermine the throughput yield (Ytp)Ytp = expDPU,Process Capability for Defect Rate,Estimation of Sigma-Capability for Defect RateDetermine the opportunities per unitDetermine the long-term defects per opportunity (d)d = defects per unit opportunities per unitDetermine the inverse cumulati
38、ve probability for d,using Calc Probability Distribution NormalZ-Score is the magnitude of the returned valueSigma-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
39、 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,Stat Quality Tools Capability Analysis (Poisson),Example 6,Defects per Unit= 0.0265194Throughput Yield= expDPU= exp0.0265194= 0.9
40、738c.f. First-Time Yield= 2 / 100= 0.02,Example 6,Define1 Inspection Unit = 125 unit length of wire i.e. Units = Length 125,Example 6A,Stat Quality Tools Capability Analysis (Poisson),Example 6A,Defects per Unit= 3.31493Throughput Yield= expDPU= exp3.31493= 0.0363c.f. First-Time Yield= 2 / 100= 0.02
41、,Example 6B,Defects per Unit= 3.31493Opportunities per Unit= 1Defects per Opportunity= 3.31493Z-Score = ?,Example 6B,1 inspection unit= 1 unit length of wireOpportunities per Unit= 1 Defects per Opportunity= 329 12,406= 0.0265Z-Score= Abs1(0.0265)= 1.935Sigma-Capability= Z-Score + 1.5= 3.435,DPU,Z-Score,s,Choice of Six Sigma Metric,
