Comparison of Pearson distribution system and response modeling methodology (RMM) as models for process capability analysis of skewed data
Article first published online: 25 JUL 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Quality and Reliability Engineering International
Special Issue: ENBIS 10
Volume 27, Issue 5, pages 681–687, July 2011
How to Cite
Shauly, M. and Parmet, Y. (2011), Comparison of Pearson distribution system and response modeling methodology (RMM) as models for process capability analysis of skewed data. Qual. Reliab. Engng. Int., 27: 681–687. doi: 10.1002/qre.1232
- Issue published online: 25 JUL 2011
- Article first published online: 25 JUL 2011
- Clements' method;
- relative mean square error;
- Pearson distribution system;
- process capability analysis;
- response modeling methodology
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. Copyright © 2011 John Wiley & Sons, Ltd.