Fundamental Changes in Theory of Duncan's Model for Economic Design of Control Charts in the Presence of Multiple Assignable Causes

One of the most widely used tools for quality engineers in quickly detecting assignable causes and monitoring processes is control charts. Duncan (in J Am Stat Assoc 51(274):228-242, 1956), in order to improve product quality and reduce the economic costs of the quality cycle, presented the first economic design of the (X) over tilde control chart in the presence of multiple assignable causes. In his model and all the economic designs derived from it, it is assumed that after the occurrence of an assignable cause, no other assignable cause occurs until the correct alarm is issued. This assumption is unrealistic and impractical in production and service processes. Therefore, in this paper, we present a realistic and practical economic design in the presence of multiple assignable causes for the (X) over tilde control chart under the Weibull shock model in industry. The numerical results of our model show well that in the previous models, the average cost per unit time of the quality cycle is severely underestimated compared to the actual value. Therefore, it is suggested that in order to eliminate the shortcomings of the previous economic design in the presence of multiple assignable causes, in future research, they should be redesigned based on our proposed model.