Joint optimization design of x control chart and maintenance under random process shift

In this paper, we propose a joint design model of control chart and maintenance policy based on Taguchi method. In most of previous studies on control chart design, it is assumed that the process shift is known and fixed, which results in the control chart optimized only for a specific process shift. To overcome the problem, we use Taguchi loss function to depict the influence of different process shift on quality cost, and consider the joint optimization design of control chart and maintenance policy under random shifts. In view of the fact that pure economic designs often lead to a large number of false alarms and also unnecessary shutdown, we add some statistical constraints in the joint model. The practical examples show that adding the statistical constraints in the economic model can control the number of false alarms without significantly increasing the total cost of the process. We also explore the effect of relevant parameters on the expected cost and control policy through simulation studies.