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

Author: Chang, Young Soon

Source: Communications in Statistics: Simulation and Computation, Volume 36, Number 4, July 2007 , pp. 921-936(16)

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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; Skewed population; Weighted standard deviation

Document Type: Research article

DOI: http://dx.doi.org/10.1080/03610910701419596

Affiliations: 1: Department of Business Administration, Myongji University, Seoul, Korea

Publication date: 2007-07-01