Bootstrap-T Technique for Minimax Multivariate Control Chart

Johnson A. Adewara, Kayode S. Adekeye

Department of Mathematical Sciences, Redeemer’s University, Redemption City, Nigeria.
Distance Learning Institute, University of Lagos, Lagos, Nigeria.

DOI: 10.4236/ojs.2012.25059                

Abstract

Bootstrap methods are considered in the application of statistical process control because they can deal with unknown distributions and are easy to calculate using a personal computer. In this study we propose the use of bootstrap-t multivariate control technique on the minimax control chart. The technique takes care of correlated variables as well as the requirement of the distributional assumptions needed for the operation of the minimax control chart. The bootstrap-t technique provides the mean θ_B of all the bootstrap estimators ** where θ_i is the estimate using the i^th bootstrap sample and B is the number of bootstraps. The computation of the proposed bootstrap-t minimax statistic was performed on the values obtained from the bootstrap estimation. This method was used to determine the position of the four control limits of the minimax control chart. The bootstrap-t approach introduced to minimax multivariate control chart helps to detect shifts in the mean vector of a multivariate process and it overcomes the computational complexity of obtaining the distribution of multivariate data.

Keywords

Bootstrap; Minimax; Multivariate Data; Control Limits; Process Control

Conflicts of Interest

The authors declare no conflicts of interest.

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