A Multivariate Synthetic Control Chart for Monitoring the Process Mean Vector of Skewed Populations Using Weighted Standard Deviations

作者：Khoo Michael B C^*; Atta Abdu M A; Wu Zhang

来源：Communications in Statistics - Simulation and Computation, 2009, 38(7): 1493-1518.

DOI：10.1080/03610910903019905

• Conforming run length
• Multivariate control charts
• Multivariate synthetic control chart
• Skewed populations
• Weighted standard deviation
• Weighted variance

This article proposes a multivariate synthetic control chart for skewed populations based on the weighted standard deviation method. The proposed chart incorporates the weighted standard deviation method into the standard multivariate synthetic control chart. The standard multivariate synthetic chart consists of the Hotelling's T(2) chart and the conforming run length chart. The weighted standard deviation method adjusts the variance-covariance matrix of the quality characteristics and approximates the probability density function using several multivariate normal distributions. The proposed chart reduces to the standard multivariate synthetic chart when the underlying distribution is symmetric. In general, the simulation results show that the proposed chart performs better than the existing multivariate charts for skewed populations and the standard T(2) chart, in terms of false alarm rates as well as moderate and large mean shift detection rates based on the various degrees of skewnesses.

• 出版日期2009
• 单位南阳理工学院