Comparing the Capability of Two Processes Using Cpm

Abstract

The indices Cp and Cpk are extensively used to assess process capability. However, they only take into account the process mean and standard deviation, but not the proximity of the process mean to the target value, T, of the process characteristic. Cpm does take into account the proximity of the process mean to the target value. We propose a method for selecting or judging the better of two suppliers or processes based on a confidence interval for the ratio Cpm1/Cpm2. Four methods of obtaining approximate confidence intervals are presented and compared, one based on the statistical theory given in Boyles (1991) and three based on the bootstrap, (referred to as SB (standard bootstrap), PB (percentile bootstrap), and BCPB (biased-corrected percentile bootstrap)). The performance was compared using simulation, which showed that, in two independent and normal process environments, Boyles's (1991) confidence interval and the SB confidence interval are more reliable than the PB and BCPB methods. A sample size of greater than 50 is recommended for selecting the most capable of two suppliers or processes.

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