Statistical Merits and Economic Evaluation of T2 Control Charts with the VSSC Scheme

Abstract

T2 control charts are used to monitor a process when more than one quality variable associated with the process is being observed. Recent studies have shown that using variable sampling size (VSS) schemes results in charts with more statistical power for detecting small to moderate shifts in the process mean vector. This paper presents an economic-statistical design of T2 control charts with variable sample size and control limits (VSSC). We build a cost model of a VSSC T2 control chart for the purpose of economic-statistical design using the model of Costa and Rahim (J. Appl. Stat. 28:875–885, 2001). This cost model constructed involves the cost of false alarms, the cost of finding and eliminating an assignable cause, the cost associated with production in an out-of-control state, and the cost of sampling and testing. We optimize this model using a genetic algorithm approach. Furthermore, VSSC and VSS T2 charts are compared with respect to the expected cost per unit time.