Robust economic-statistical design of multivariate exponentially weighted moving average control chart under uncertainty with interval data

The cost parameters in economic-statistical models of control charts are usually assumed to be deterministic in the literature. Considering uncertainty in the cost parameters of control charts is very common in application. So, several researchers used scenario-based approach for robust economic-statistical design of control charts. In this paper, we specifically concentrate on the Multivariate Exponentially Weighted Moving Average (MEWMA) control chart and consider interval uncertainty in the cost parameters of the MEWMA control chart and develop a robust economic-statistical design of the MEWMA control chart by using interval robust optimization technique. Meanwhile, the Lorenzen and Vance cost function is used, and to calculate the average run length criterion, the Markov chain approach is applied. Then, genetic algorithm for obtaining optimal solution of the proposed robust model is used and effectiveness of this model is illustrated through a numerical example. Also, a comparison with certain situation of the cost parameters is performed. Finally, a sensitivity analysis is done to investigate the effect of changing the intervals of cost parameters of the Lorenzen and Vance model on the optimal solutions. Furthermore, a sensitivity analysis on the other certain cost parameters of the Lorenzen and Vance model is done.