【正文】 Information, the way you want itProcess Capability Analysis (Measure Phase) Scope 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 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) 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 “outofcontrol” Process 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 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 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 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) Three Types of Limits Distribution of Individual Values Distribution of Sample Averages Process Capability Indices Two measures of process capability ? Process Potential – Cp ? Process Performance – Cpu – Cpl – Cpk Process Potential The Cp index assesses whether the natural tolerance (6?) of a process is within the specification limits. ????6LSLUSLToleranceNaturalTolerancegEngineerinC pProcess 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 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 pares the allowable spread (USLLSL) against the process spread (6?). It fails to take into account if the process 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. ????3USLCpu ????3LSLpl ? ? ?????3NSLC,CMinimumCplpupkProcess Performance Cpk Reject Rate – % – % – % – ppm – ppm – ppm 794 – 1589 ppb 170 – 340 ppb 33 – 67 ppb 6 – 12 ppb 1 – 2 ppb Process Performance a) Process is highly capable (Cpk) b) Process is capable (Cpk=1 to ) c) Process is not capable (Cpk1) a) Cp = 2 Cpk = 2 b) Cp = 2 Cpk = 1 c) Cp = 2 Cpk 1 Example 1 Specification Limits : 4 to 16 g Machine Mean Std Dev (a) 10 4 (b) 10 2 (c) 7 2 (d) 13 1 Determine the corresponding Cp and Cpk for each machine. Example 1A ? ? 4166 LSLUSLC p ?????? ? ? ? ? 43410。431016Min3LSL。3USLMinCpk ??????? ????????????????Example 1B ? ? 4166 LSLUSLC p ?????? ? ? ? ? 23410。231016Min3LSL。3USLMinCpk ??????? ????????????????Example 1C ? ? 4166 LSLUSLC p ?????? ? ? ? ? 2347。23716Min3LSL。3USLMinCpk ??????? ????????????????Example 1D ? ? 4166 LSLUSLC p ?????? ? ? ? ? 13413。131316Min3LSL。3USLMinCpk ??????? ????????????????Process Capability For a normally distributed characteristic, the defective