Combining process capability indices from a sequence of independent samples

Process capability indices such as C_p, C_pk and C_pm have been widely used in manufacturing for process assessment and for evaluation of purchasing decisions. Quality engineers and process operators are often asked to summarize the quality of a process by combining a sequence of C_pk or C_pm. This paper compares three different methods for combining the estimates of the process capability indices C_pk, C_pm and C_pmk from a sequence of independent samples. The criterion of minimum mean-squared-error (MSE) is applied. We find that, in general, methods for the combination of sample process capability indices based on the overall sample mean and pooled sample variance give smaller MSE than those based on weighted averages of the estimates of process capability indices.