Adjusted action limits for Cpm based on departures from normality

Abstract

The process capability index Cpm is used to asses the ability of a process to be clustered around a target. As Cpm is not traditionally used to provide insights into process yield, the Cpm parameter does not require 6 σ to reflect a precise number of non-conforming. Therefore, unlike other capability indices including Cp, Cpu, Cpl, Cpk and Cpmk, that are used primarily to examine process yield (parts per million non-conforming), Cpm is not distributionally sensitive. Robustness studies for those process capability indices whose magnitudes are translated into process yield are meaningless as the parameters are sensitive to departures from normality. Regardless of how robust the estimator maybe, its associated process yield is not stable with respect to shifts in the underlying distribution and hence any robustness claims carry little meaning. Since Cpm assesses clustering around the target using Euclidean distance, the robustness of an estimator of Cpm to distributional assumptions and the resulting impact on the inferences, can be investigated. The impact of skewness and kurtosis on the tail probabilities of g ( C ^ pm ) are quantified and the associated limits modified to provide stochastically corrected confidence bounds and action limits. An example from the printing industry is used to illustrate the adjustments and resulting inferences.