A Novel Differential Evolution Algorithm with Q-Learning for Economical and Statistical Design of X-Bar Control Charts

This paper presents a novel differential evolution algorithm with Q-Learning (DE_QL) for the economical and statistical design of X-Bar control charts, which has been commonly used in industry to control manufacturing processes. In X-Bar charts, samples are taken from the production process at regular intervals for measurements of a quality characteristic and the sample means are plotted on this chart. When designing a control chart, three parameters should be selected, namely, the sample size (n), the sampling interval (h), and the width of control limits (k). On the other hand, when designing an economical and statistical design, these three control chart parameters should be selected in such a way that the total cost of controlling the process should be minimized by finding optimal values of these three parameters. In this paper, we develop a DE_QL algorithm for the global minimization of a loss cost function expressed as a function of three variables n, h, and k in an economic model of the X-bar chart. A problem instance that is commonly used in the literature has been solved and better results are found than the earlier published results.