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 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.,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 Rate 1.00 0.270 % 1.33 0.007 % 1.50 6.8 ppm 2.00 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 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.,Process Performance,Cpk Reject Rate 1.0 0.13 0.27 % 1.1 0.05 0.10 % 1.2 0.02 0.03 % 1.3 48.1 96.2 ppm 1.4 13.4 26.7 ppm 1.5 3.4 6.8 ppm 1.6 794 1589 ppb 1.7 170 340 ppb 1.8 33 67 ppb 1.9 6 12 ppb 2.0 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 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,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 Machine Mean Std 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 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 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 Design to reduce variation,Experimental Design to center mean to re