Simultaneous Monitoring of Mean and Variance Through Optimally Designed SPRT Charts

Abstract

Four essential properties that a control chart must have are applicability, high sensitivity for detecting shifts, cost-optimality, and the capability of jointly controlling all the important parameters that characterize a process. This paper introduces a quality monitoring system design for jointly monitoring the mean and the variance of a Gaussian process. The design of this monitoring system, the Economic Mean and Variance —Sequential Probability Ratio Tests (EMV-SPRT) charts, possesses all of the desired properties mentioned above. The applicability of the design comes from the utilization of assumptions that fit many actual processes. The sensitivity is a consequence of the use of SPRT. The determination of the design parameters through an economic model ensures cost optimality.

This study extends the original concept of SPRT in order to deal with two parameters. The resulting monitoring scheme benefits from the fact that SPRT charts indicate in-control or out-of-control states using the minimum number of sample units. In addition to having this inherent optimality, the EMV-SPRT sampling procedure uses neither a predetermined sample size, nor a set of predetermined bounds for Type I and Type II errors: instead, it uses an economic approach. The EMV-SPRT design is compared numerically with two other relevant designs that exist in the literature. The sensitivity of the EMV-SPRT design with respect to some of the key input parameters is also studied.