A comparison of multivariate control charts for skewed distributions using weighted standard deviations


  • Michael B.C. Khoo
  • Sin Yin Teh
  • May Yin Eng




Multivariate control charts, Skewed distributions, Weighted standard deviations, WSD 2T, WSD MEWMA, WSD MCUSUM,


The quality of a manufacturing process usually depends on more than one quality characteristic. Thus, most process monitoring data are multivariate in nature. The assumption that the underlying process follows a multivariate normal distribution is usually required by most multivariate quality control charts. However, in most process monitoring situations, the multivariate normality assumption is often violated. Multivariate control charts for skewed distributions have been suggested to enable process monitoring to be made when the underlying process distribution is skewed. Among the recent heuristic multivariate charts for skewed distributions suggested in the literature are those based on the weighted standard deviation (WSD) approach. This paper compares the performances of three multivariate charts for skewed distributions incorporating the WSD method, namely, the WSD T 2 , WSD multivariate cumulative sum (WSD MCUSUM) and WSD multivariate exponentially weighted moving average (WSD MEWMA) charts. These heuristic charts are compared based on the multivariate lognormal, gamma and Weibull distributions. The charts’ performances are evaluated using the false alarm rates, computed via a Monte-carlo simulation. The chart with the lowest false alarm rate for most of the skewness levels and sample sizes will be identified as the chart having the best performance.


A. Mitra, Fundamentals of Quality Control and Improvement, 2nd Ed. New Jersey: Prentice Hall (1998).

J.J., Jr. Pignatiello and G.C. Runger, J Qual Technol, 22 (1990) 173-186.

Y.S. Chang and D.S. Bai, Qual Reliab Eng Int, 20 (2004) 31-46. [4] Y.S. Chang, Comm. Statist. Simulation Comput., 36 (2007) 921-936.