An economic model for determining the optimal quality and process control policy in a queue-like production system

This paper interrelates and synthesizes the economic design of quality and process control policy and the management of a production system described in terms of an M/G/X queue. A mathematical model is developed to determine the optimal quality and process control policy when both the quality and quantity issues in the production system are considered. The optimal control policy is defined as the one that maximizes the expected profit per unit time over an infinite horizon. Hypothetical data is used to illustrate the impact of on-line control policies on the operating characteristics of the production process.

For a given control policy, it is shown that the expected profit per unit time of the production system can be increased by either improving the reliability of the production system, increasing the arrival rate of incoming jobs, increasing the system's processing rate, or shortening the system's shutdown time. The results also indicate that the larger the performance difference between the in-control and the out-of-control states, the greater the amount of effort should be involved in quality and process control. Finally, it is important for the capacity design of a production system to take into account the requirrments for both quality control and process adjustment.