Multi-objective Markov-based economic-statistical design of EWMA control chart using NSGA-II and MOGA algorithms

The exponentially weighted moving average (EWMA) control charts are useful for detecting small shifts in the process mean. In this paper, we investigate multi-objective economic-statistical design of the EWMA control charts and propose two evolutionary algorithms including non-dominated sorting genetic algorithm (NSGA-II) and multi-objective genetic algorithm (MOGA) to determine the optimal chart parameters. The cost function used in this paper is Lorenzen and Vance cost function. We also used quadratic Taguchi loss function to determine the costs of producing non-conforming items under both in-control and out-of-control situations. The average run length values in both in-control and out-of-control states are computed by using Markov chain approach. A numerical example is applied to compare the results of proposed algorithms in finding the Pareto optimal solution of the multi-objective economic-statistical model. Finally, a sensitivity analysis on the economic and the statistical criteria of the EWMA control chart under both proposed algorithms is conducted.