Statistical economic design of an X control chart

The paper presents the economic design of an X control chart preserving the statistical proprieties of the chart. The classical algorithms of economic design are based on the minimisation of a cost function which depends on the sample size n, the width of control limits k, and the time interval between samples h: the statistical proprieties, represented by ATS(1) and ATS(2) are obtained values. It is possible to achieve a control chart that reaches the economic goal but has an insufficient ATS(1) or ATS(2). For this reason an appropriate design is necessary before the chart is used. In this paper a new approach, based on an evolutionary algorithm, to solve this problem is proposed. The design of the chart has been developed considering the objective function, which directly handles on alpha and beta values and permits to consider both economic and the statistical properties. The proposed approach has been compared to a well-known heuristic algorithm, a sensitivity analysis has been carried out too. The obtained results show the effectiveness of the evolutionary algorithm.