A generalized economic model for joint determination of production run, inspection schedule and control chart design

This paper presents a generalized model for a continuous production process for simultaneous determination of production quantity, inspection schedule and control chart design, with a non-zero inspection time for false alarms. Traditionally, the quality control problem and the inventory control problem have been viewed as two separate problems. Rahim (1994) developed an economic model for joint determination of production quantity, inspection schedule, and control chart design for a typical production process which is subject to a non-Markovian random shock. The model consists of the following cost components: (1) the production setup cost, (2) the inventory holding cost, and (3) the cost of maintaining the quality of the product under the surveillance of an (x) over bar-chart. The optimal production quanity, the optimal inspection schedules, and the economic design parameters of the control charts were determined by striking a balance among these costs. For mathematical simplicity, it was assumed that production ceases only if the process was found to be out-of-control. However, in reality, this assumption may be inapplicable in many industrial situations. In many production processes the machine must be shut down when a search for the assignable cause is being carried out, even though occasionally the alarm turns out to be false. The purpose of this paper is to generalize the above model to cases where production ceases not only for a true alarm but also for a fixed amount of time whenever there is a false alarm. Examples of Weibull shock models are used to illustrate the proposed generalized model.