An integrated economic model for inventory and quality control problems

Abstract

This paper develops an integrated economic model for inventory and quality control problems. The joint X¯ and R charts are used to control the production process, and this is combined with the determination of the economic production quantity in production processes. The production process is subject to an assignable cause which shifts the process from an in-control state to an out-of-control state. Shifts in both the process mean and the process variance are considered. 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 the process mean and the process 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.

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