Performance evaluation of control chart for multiple assignable causes using genetic algorithm

With a view to monitoring and controlling manufacturing processes in industries, control charts are widely used and needed to be designed economically to achieve minimum quality costs. Many authors have studied the economic design of the $ \overline{X} $ control chart after Duncan (J Am Stat Assoc 51(274):228–242, 1956) first proposed the economic model of the $ \overline{X} $ control chart for a single assignable cause. But, in practice, multiple assignable causes are more logical and realistic. Moreover, the economic design does not consider statistical properties like bound on type I and type II error, and average time to signal (ATS). This paper focuses on evaluating the performance of genetic algorithm (GA) in pure economic and economic statistical design of the $ \overline{X} $ control chart for multiple assignable causes. The performances of GA are demonstrated by comparing its result with the previously proposed grid search technique for a numerical example. The Duncan model of multiple assignable causes is adopted to formulate objective function, and the computation is achieved by approximation through a numerical method named Simpson's 1/3 rule. Comparison distinctly shows the superiority of GA over grid search results for economic statistical design.