【正文】 i k 1j ij42m1ik1j ij4Overall ???????? ? ?? ? ? ?? ?Process Capability Analysis 36 Information, the way you want itEstimating ?Within and ?Overall The within variation ?Within may be estimated by one of the following: (a) Rbar Method where d2 is a Shewhart constant = ?(k) (b) Sbar Method where c4 is a Shewhart constant = ?(k) (c) Pooled Standard Deviation Method In MiniTab, the Pooled Standard Deviation is the default method. 2Wit hin dR? ?4With in cS? ? ? ? ? ? ?? ? ? ? ? ?1n1n1n S1nS1nS1nc1?m212mm2222114Wit hin ????????????????Process Capability Analysis 37 Information, the way you want itEstimating ?Within and ?Overall In cases where there is only 1 observation per subgroup (. 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 : 1iii XXMR ??? 2Withi n dMR? ??~ 2Withi n?Process Capability Analysis 38 Information, the way you want itExample 3 The length of a camshaft for an automobile engine is specified at 600 177。3USLMinCpk ??????? ????????????????Process Capability Analysis 23 Information, the way you want itExample 1D ? ? 4166 LSLUSLC p ?????? ? ? ? ? 13413。3USLMinCpk ??????? ????????????????Process Capability Analysis 22 Information, the way you want itExample 1C ? ? 4166 LSLUSLC p ?????? ? ? ? ? 2347。3USLMinCpk ??????? ????????????????Process Capability Analysis 21 Information, the way you want itExample 1B ? ? 4166 LSLUSLC p ?????? ? ? ? ? 23410。Information, the way you want itProcess Capability Analysis (Measure Phase) Process Capability Analysis 2 Information, the way you want itScope of Module ? Process Variation ? Process Capability – Specification, Process and Control Limits – Process Potential vs Process Performance ? ShortTerm vs LongTerm Process Capability ? Process Capability for NonNormal Data – CycleTime (Exponential Distribution) – Reject Rate (Binomial Distribution) – Defect Rate (Poisson Distribution) Process Capability Analysis 3 Information, the way you want itProcess 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 (unitunit variation) ? between lots (lotlot variation) ? between lines (lineline variation) ? across time (timetime variation) ? measurement error (repeatability reproducibility) Process Capability Analysis 4 Information, the way you want itTypes 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” Process Capability Analysis 5 Information, the way you want itTypes 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 “outofcontrol” Process Capability Analysis 6 Information, the way you want itProcess Capability Process Capability is the inherent reproducibility of a process’s 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 Analysis 7 Information, the way you want itProcess Capability Process Capability studies can ? indicate the consistency of the process output ? indicate the degree to which the output meets specifications ? be used for parison with another process or petitor Process Capability Analysis 8 Information, the way you want itProcess Capability vs Specification Limits a) b) c) a) Process is highly capable b) Process is marginally capable c) Process is not capable Process Capability Analysis 9 Information, the way you want itThree Types of Limits Specification Limits (LSL and USL) ? created by design engineering in response to customer requirements to specify the tolerance for a product’s 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) Process Capability Analysis 10 Information, the way you want itThree Types of Limits Distribution of Individual Values Distribution of Sample Averages Process Capability Analysis 11 Information, the way you want itProcess Capability Indices Two measures of process capability ? Process Potential – Cp ? Process Performance – Cpu – Cpl – Cpk Process Capability Analysis 12 Information, the way you want itProcess Potential The Cp index assesses whether the natural tolerance (6?) of a process is within the specification limits. ????6LSLUSLToleranceNaturalTolerancegEngineeri nC pProcess Capability Analysis 13 Information, the way you want itProcess Potential A Cp of indicates that a process is judged to be “capable”, . if the process is centered within its engineering tolerance, % of parts produced will be beyond specification limits. Cp Reject Rate % % ppm ppb Process Capability Analysis 14 Inf