A generalized model for multiplicity-cause economic and economic statistical design of (X)over-bar-control charts with proportional hazards shock model

One of the most popular approaches to analyze failure time data in the presence of influential covariates is proportional hazards model. In this article, the multiplicity-cause economic design of (X) over bar -control charts are extended by employing this family as the shock model of the process. For illustration, the Weibull and the Chen lifetime distributions are applied to obtain the optimal design parameters, that is, the sample size, the sampling intervals, and the width coefficient of control limits. In both economic and economic statistical designs, the numerical results show that the multiplicity-cause model outperforms the single one in terms of the loss-cost value.