Optimum Multiple and Multivariate Poisson Statistical Control Charts

Abstract

This paper deals with the simultaneous statistical process control of several Poisson variables. The practitioner of this type of monitoring may employ a multiple scheme, i.e. one chart for controlling each variable, or may use a multivariate scheme, based on monitoring all the variables with a single control chart. If the user employs the multivariate schemes, he or she can choose from, for example, three options: (i) a control chart based on the sum of the different Poisson variables; (ii) a control chart on the maximum value of the different Poisson variables; and (iii) in the case of only two variables, a chart that monitors the difference between them. In this paper, the previous control charts are studied when applied to the control of p = 2, 3 and 4 variables. In addition, the optimization of a set of univariate Poisson control charts (multiple scheme) is studied. The main purpose of this paper is to help the practitioner to select the most adequate scheme for her/his production process. Towards this goal, a friendly Windows (c) computer program has been developed. The program returns the best control limits for each control chart and makes a complete comparison of performance among all the previous schemes.