Economic and economic-statistical designs of MEWMA control charts—a hybrid Taguchi loss, Markov chain, and genetic algorithm approach

Abstract

Economic design of multivariate exponentially weighted moving average (MEWMA) control charts for monitoring the process mean vector involves determining economically the optimum values of the three control parameters: the sample size, the sampling interval between successive samples, and the control limits or the critical region of the chart. In the economic-statistical design, constraints (including the requirements of type I error probability and power) are added such that the statistical property of the chart is satisfied. In this paper, using the multivariate Taguchi loss approach, the Lorenzen–Vance (Technometrics 28:3-10, 1) cost function of implementing the control chart is extended to include intangible external costs along with the in-control average run length (ARL0) and out-of-control average run length (ARL1) as statistical constraints. A Markov chain model is then developed to estimate the ARLs and a genetic algorithm whose parameters are optimally obtained by design of experiments is used to solve the model and estimate the optimum values of the control chart parameters. A numerical example and a sensitivity analysis are provided to illustrate the solution procedure and to investigate the effects of cost parameters on the optimal designs. The results show that the proposed economic-statistical design of the chart has better statistical properties in comparison to the economic design while the difference between the costs is negligible.