Multivariate CUSUM and EWMA Control Charts for Skewed Populations Using Weighted Standard Deviations

Abstract

This article proposes a heuristic method of constructing multivariate cumulative sum and exponentially weighted moving average control charts for skewed populations based on the weighted standard deviation method which adjusts the variance–covariance matrix of quality characteristics and approximates the probability density function using several multivariate normal distributions. These control charts, however, reduce to the conventional control charts when the underlying distribution is symmetric. In-control and out-of-control average run lengths of the proposed control charts are compared with those of the conventional control charts for multivariate lognormal and Weibull distributions. Simulation results show that considerable improvements over the standard method can be achieved when the underlying distribution is skewed.

Keywords:

• Multivariate cumulative sum control chart
• Multivariate exponentially weighted moving average control chart
• Skewed population
• Weighted standard deviation

Mathematics Subject Classification:

• 62P30
• 62E17

Notes

(1) γ _i : skewness of ith quality characteristic X _i .

(2) STD: Standard Method.

(3) WSD: WSD Method.

(1) Cases are depicted in Fig. 5(a).

(1) Cases are depicted in Fig. 5(b).