Statistical Economic Design of an X Control Chart

Abstract

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 ATS₁ and ATS₂ are obtained values. It is possible to achieve a control chart that reaches the economic goal but has an insufficient ATS₁ or ATS₂. 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 α and β 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.