Determining an optimal production run length with an extended quality control policy for an imperfect process

In this paper an extended quality control policy is proposed for determining the optimal production run length, where the production system is subjected to random deterioration from an in-control state to an out-of-control state and in which the elapsed time until the process shift is assumed to be a general shift distribution. To minimize the quality-related cost for a given production run length, a quality control policy for product inspection, repair and salvage was rigorously developed. The conditions for the two most commonly used inspection policies, namely no inspection or full inspection, were explored. Also, our proposed quality control policy is an extension of several previously reported proposals. In our proposed quality control policy, the optimal production run length can be obtained by minimizing the expected total cost per product per production cycle, which includes the costs of setup, inventory holding, process maintenance and quality control. Herein, we provide an illustrated numerical example to show how the use of our proposed quality control model for determining optimal production run length results in a lower cost per product than the model proposed by Hu and Zong (2009).