Multi-objective genetic algorithm for economic statistical design of X control chart

Control charts are widely used for monitoring the quality of a product or a process. Their implementation cost motivates researchers to design them with the lowest cost and most desirable statistical properties. Usually, the cost function is optimized subject to statistical properties. However, the cost function also depends on statistical properties, and minimizing it as the only objective is not an efficient method of economic statistical design of control charts. In this paper, cost function, as well as statistical properties, including probability of Type I error, power of X control chart, and Average Time to Signal (ATS), are considered as objectives; the corresponding constraints are also used. Then, a Multi-Objective Genetic Algorithm for Economic Statistical Design (MOGAESD) is proposed for identifying the Pareto optimal solutions of control chart design. The preferred solution is selected by the designer. The performance of the proposed method is compared through some numerical examples reported in the literature. The results show that the proposed approach is effective.