A Performance Analysis of the Minimax Multivariate Quality Control Chart

Abstract

A performance analysis of three different Minimax control charts is performed with respect to their Chi-Square control chart counterparts under several different conditions. A unique control chart must be constructed for each process described by a unique combination of quality characteristic mean vector and associated covariance matrix. The three different charts under consideration differ in the number of quality characteristic variables of concern. In each case, without loss of generality the in-control quality characteristic mean vector is assumed to have zero entries and the associated covariance matrix is assumed to have non-negative entries. The performance of the Chi-Square and Minimax charts are compared under different values of the sample size, the probability of a Type I error, and selected shifts in the quality characteristic mean vector. Minimax and Chi-Square charts that are compared share identical in-control average run lengths (ARL) making the out-of-control ARL the appropriate performance measure. A combined Tausworthe pseudorandom number generator is used to generate the out-of-control mean vectors. Issues regarding multivariate uniform pseudorandom number generation are addressed.