Double Objective Economic Statistical Design of the VPT2 Control Chart: Wald’s identity approach

E-print/Working paper (n.d.)

Recent studies have shown that applying the control chart by using a variable parameters (VP) scheme yields more rapid detection of assignable causes than the classical method of taking fixed sample sizes ... [more ▼]

Recent studies have shown that applying the control chart by using a variable parameters (VP) scheme yields more rapid detection of assignable causes than the classical method of taking fixed sample sizes at fixed intervals of time. In this paper, the problem of economical statistical design of the VP T2 control chart is considered as a double-objective minimization problem with the statistical objective adjusted average time to signal and the economic objective expected cost per hour. Then we strive to find the Pareto-optimal designs in which the two objectives are met simultaneously by using a multi-objective Genetic Algorithm or GA. Through an illustrative example, we show that relatively large benefits accrue to the VP method relative to the classical policy; further another advantage of our approach is to provide a list of alternative solutions that can be explored graphically. This then ensures flexibility and adaptability, an important attribute of contemporary control chart design. [less ▲]