### The Optimization with The Genetic Algorithm Approach of the Multi-objective, Joint Economical Design of the (x)over-bar and R Control Charts

Abstract

In this paper, a model has been developed for the (x) over bar -chart showing the shifts in the process mean and R-chart showing those in the process variability. The model involves such parameters as the sample size, n, the sampling frequency, h, and the range of the control limits, k(1) and k(2). The aim is to find the values of n, h, k(1) and k(2) minimizing the cost junction. This is adequate to reach the economic objectives. However, this paper is aimed at meeting the statistical objectives. The statistical objectives include minimizing the Type I error and the enhancing the testing power. Hence, the economic model has been handled as a multi-objective optimization problem involving the statistical objectives. Nonetheless, clue to the fact that it is difficult, using classical methods, to solve such economic models that have the nature of a complex function, Genetic Algorithms (GAs) were used The results are summarized in tables after they have been compared with those in the published literature. It is understood that the results obtained by GA are better than those in the literature and that they are more likely to reach the statistical objectives.