Comparison of Pearson distribution system and response modeling methodology (RMM) as models for process capability analysis of skewed data

Clements' approach to process capability analysis for skewed distributions, based on fitting the Pearson distribution system to data, is widely used in industry. In this paper we compare the accuracy of the Pearson system and the RMM (response modeling methodology) distribution, as distributional models for process capability analysis of non-normal data. The accuracy of the estimates of Cp and CPU is measured by the relative mean square errors. Three factors that may affect the accuracy of RMM and Pearson are examined: the data-generating distribution (Weibull, log-normal, gamma), the skewness (0.5, 1.25, 2) and the sample size (50, 300, 2000). The results show that RMM consistently outperforms Pearson, even for samples from gamma, which is a special case of Pearson. This implies that when observations are visibly skewed yet their underlying distribution is unknown, RMM estimators for Cp and CPU take account of the information stored in the data more precisely than the Pearson model, and may therefore constitute a preferred distributional model to pursue in process capability analysis.