An integrated optimization model for inventory and quality control problems (Q959493)

In this paper, we develop an integrated economic model for inventory and quality control problems, extending the work of \textit{M. A. Rahim} [IIE Trans. 26, No. 6, 2--11 (1994) and Rahim and \textit{M. Ben-Daya} [Int. J. Prod. Res. 36, No. 1, 277--289 (1998; Zbl 0951.90515)]. The production process is subject to an assignable cause which shifts the process from an in-control state to an out-of-control state. We consider the shifts in both the process mean and the process variance. When a signal for an assignable cause is triggered, a search is initiated and is terminated upon finding the cause within a pre-specified target time. The process is then brought back to an in-control state by repair. However, if the assignable cause is not discovered within the pre-specified time, production is allowed to continue until the next sampling or warning, whichever occurs first. In this case, either the alarm is considered to be false with a probability of Type I error, or the assignable cause has not been eliminated with a probability of Type II error. In the latter case, the process produces products in an out-of-control state until the next sampling or warning, whichever occurs first. However, this state does not indicate any severe damage to the system. Joint X and R charts are used for monitoring both process mean and variance. Under these conditions, a generalized economic model for the joint determination of production quantity, an inspection schedule, and the design of the X and R control charts are developed. A direct search optimization method is used to determine the optimal decision variables of the economic model.