Economic and economic statistical design of T2 control chart with two adaptive sample sizes

The Hotelling's T² control chart, a direct analogue of the univariate Shewhart X̄ chart, is perhaps the most commonly used tool in industry for simultaneous monitoring of several quality characteristics. Recent studies have shown that using variable sampling size (VSS) schemes results in charts with more statistical power when detecting small to moderate shifts in the process mean vector. In this paper, we build a cost model of aVSS T² control chart for the economic and economic statistical design using the general model of Lorenzen and Vance [The economic design of control charts: A unified approach, Technometrics 28 (1986), pp. 3-11]. We optimize this model using a genetic algorithm approach. We also study the effects of the costs and operating parameters on theVSS T² parameters, and show, through an example, the advantage of economic design over statistical design forVSS T² charts, and measure the economic advantage ofVSS sampling versus fixed sample size sampling.