09Capability(制程能力)ppt課件

1、Process Capability andThe Standard TransformChampion TrainingUSLImproveAnalyzeMeasure ControlAssessing Process Capability for Variable Data Verify Specification and Measurement System Take a short term or long term sample Verify Process Stability Calculate Cp, Cpk, Pp, Ppk, DPU and PPM Calculate Z-s

2、core short term and long term (Sigma Level)Verify SpecsTakeSampleVerifyProcessStabilityCalculateCp, Cpk,Pp, Ppk, DPU& PPMCalculateZ-stZ-lt.General Form:This transform produces a value from a distribution where the Mean = 0 and = 1. The value indicates how far the number is from the mean in units of

3、standard deviations. For example, if Z = 2, that would say that the number in question is 2 standard deviations away from the Mean.For estimating our yield for a process, we will substitute the Lower Spec Limit (LSL) and the Upper Spec Limit (USL) for x. By using this method, we can calculate the pr

4、oportion of product that is out-of-spec based on that products Output Mean and .Let s look at an example.The Standard Transform.Z-Transform ExampleMean = 1.03 LSL = 0.90 = 0.0573 USL = 1.10 1.00.90.87006005004003002001000rawFrequencyUSLLSL.Z-TransformThe task is to determine estimates of th

5、e proportion of the normal curve that is outside the upper and lower specification limits. We do that by calculating Z-score for each spec limit.We can now calculate the areas below the lower spec and above the upper spec using the normal probability function.ExampleStandard Score DistributionRaw Sc

6、ore Distribution1.00.90.87006005004003002001000rawFrequencyUSLLSL43210-1-2-3-45004003002001000C2FrequencyLSLUSL.ExampleThe Fraction Outside the Spec Limits can be determined by using Normal Table or Minitab Functions.Where do we get the probabilities? The Normal Table or Minitab.CalcProbabi

7、lity DistributionNormalBasic StatisticsDescriptive StatisticsDescriptive StatisticsVariable N Mean Median Tr Mean StDev SE MeanLongtRel 200 3.7403 3.7650 3.7349 0.3771 0.0267ShortRel 50 3.6552 3.6800 3.6539 0.3373 0.0477Variable Min Max Q1 Q3LongtRel 2.9800 4.6500 3.4200 3.9800ShortRel 2.9800 4.2500

8、 3.2975 3.9050What is the difference between the Short Term and the Long Term St. Dev.? .The Idea of Rational SubgroupsGoal: To establish a sampling window small enough to exclude systematic nonrandom influences.Intended Result: Data exhibiting only common cause variation within groups of n items an

9、d special cause (if it exists) variation between groups.If done correctly, averaged (Pooled) sigmas from the subgroups give us a good estimate of our best case process capability based on the current process. If there is a big difference between the pooled standard deviation and the standard deviati

10、on based on the total data set, we have shifts in the process mean or sigma over time.An Example of Rational SubgroupsHow does the Within Groups sigma relate to the Total sigma? Hint: You can run the Descriptive Stat procedure for the total data set and then run it again using the BY variable option

11、 with Shift as the variable.Open the file Ratsubgrmtw. Plot the data using the Time Series plot. Use the Reference option under Frame for graphing shift boundary lines.Demonstration of Rational SubgroupsShift is the Grouping Variable.Descriptive Statistics ( Stat Basic Statistics Descriptive Statist

12、ics)Variable N Mean Median TrMean StDev SEMeanOutput 32 2.376 2.327 2.376 0.798 0.141Now run Descriptive Statistics using the By Variable function : Stat Basic Statistics Descriptive Statistics ( Variables : Output , By variable : Shift ) Descriptive StatisticsVariable Shift N Mean Median TrMean StD

13、ev SEMeanOutput 1 8 1.6026 1.6177 1.6026 0.1817 0.0642 2 8 3.1020 3.1129 3.1020 0.2047 0.0724 3 8 1.6150 1.6284 1.6150 0.1583 0.0560 4 8 3.1831 3.2331 3.1831 0.1708 0.0604Results of Descriptive StatisticsWhat implication does this have in studying process capability? What sigma represents the real p

14、rocess capability? What sigma represents the potential process capability?.Components of Variation and Rational SubgroupsTotal Sum of Squares = Between Grp SS + Within Grp SSTotal VariabilityMean Shift VariabilityPooled Within Grps Variability.Components of Variation and Rational SubgroupsCapability

15、PrecisionAccuracyTotal Sum of Squares =Between Grp SS +Within Grp SS.Visualizing the Process DynamicsOver time, a “typical process will shift and drift by approx. 1.5“Short Term CapabilityLSLUSLTTime 1Time 2Time 3Time 4Pooled std. dev.Overall std. dev.WITHIN GROUPBETWEEN GROUPInherent Capability of

16、the ProcessSustained Capability of the Process “Long Term Capability.Visualizing the Components of VariabilityUSLLSLThe effect of process shift over time is 1.5 sigma 1j=2j)X-X(ng2g1jn1=ijij)X(X=-2g1j=n1=iij)XX(-.3 Sigma Process No Mean Shift.3 Sigma Process Mean Shift of 1.5 sigma.Six Sigma Process

17、 No Mean Shift.Six Sigma ProcessMean Shift of 1.5 sigma.Short Term Process Capability RatiosProcess Width+3-3TLSLUSLstCp assumes the Process is CenteredUSL - LSL 6Cp =st.Short Term Process Capability RatiosCpk accounts for the Mean Shift in the Processstst Cpk = Cp(1-k) whereT - X 3K =st.Long Term P

18、rocess Capability RatiosProcess Width+3-3TLSLUSLUSL - LSL 6Pp =ltPp assumes the Process is CenteredPp( Maximum Allowable Range of Characteristic )ltZ=3Pp( Normal Variation of the Process ).Long Term Process Capability RatiosPpk accounts for the Mean Shift in the Process Ppk = Pp(1-k) whereT - X 3K =

19、ltltltPMin( X-LSL3USL-X3pk,)Z=3Pplt.The Process Improvement Plan calls for performing a Short-term Capability study during the Measurement Phase to establish the process baseline. Minitabs process capability functions allow you options on what std. dev. to use in the capability ratio calculations:Sh

20、ort- term Capability uses the within subgroup standard deviation calculated in Minitab. This measures the “instantaneous capability and may be used to establish process entitlement.Long- term capability uses the Overall Standard Deviation (Total): By using the overall standard deviation, you get the

21、 best estimate of your long term capability.Process Improvement Plan.Assessing Process Capability for Attribute Data Verify Attribute Measurement System Count process defects and total units processed Calculate PPM and DPU (Defects per unit) Calculate Z-score short term and long term (Sigma Level)Co

22、unt Process DefectsCalculatePPM & DPUCalculateZ-stZ-lt.Assessing Process Capability for Attribute DataCalculate DPU, PPM and Z-score for the following process: Total defects = 976 Total units produced = 9,000 DPU = 0.108444 PPM = 108,444 Zlt = 1.23 Zst = 1.23 + 1.50 = 2.73 .What Does All This Mean?Short-TermCp to RTYCp (from Minitab for short-term study) (assumes the process is centered)ZST = 3 * Cp (Page 8.14