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 pr ocess for simultaneous determination of production quantity, inspectio n schedule and control chart design, with a non-zero inspection time f or false alarms. Traditionally, the quality control problem and the in ventory control problem have been viewed as two separate problems. Rah im (1994) developed an economic model for joint determination of produ ction quantity, inspection schedule, and control chart design for a ty pical production process which is subject to a non-Markovian random sh ock. The model consists of the following cost components: (1) the prod uction 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 inspect ion schedules, and the economic design parameters of the control chart s were determined by striking a balance among these costs. For mathema tical simplicity, it was assumed that production ceases only if the pr ocess was found to be out-of-control. However, in reality, this assump tion may be inapplicable in many industrial situations. In many produc tion processes the machine must be shut down when a search for the ass ignable 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 alar m 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.