An ongoing production process produces defective parts at random intervals. Each defective part provides a learning opportunity which the decision maker may use to improve the process by investing resources to identify and remove the causes of the defective. For various cost criteria, it is optimal to invest in learning until the probability of producing a defective becomes sufficiently small. This policy has economic interpretations in terms of marginal benefits. In addition, the optimal policy for expected discounted present cost has an interpretation in terms of tradeoffs between "cost of failure" and "cost of prevention". The shape of the tradeoff curve gives insight into the controversy between the traditional and zero defects views towards cost of quality.production control, process improvement, dynamic programming

We study the control of a production process which moves at a random time from an in-control state to an out-of-control state where an increased number of defective units is produced. After each unit is produced, a decision maker has three choices: continue production, invest in routine maintenance that restores the process to control, and invest in a more expensive learn maintenance that, in addition, may decrease the tendency of the process to go out of control. The optimal policy structure is shown to be of the control-limit type with the property that learning is not optimal if the tendency of the process to go out of control is small enough. If there is no opportunity to inspect the process's output, an optimal policy can be interpreted as a fixed production run. For this case an exact algorithm is developed. When the process's output is inspected, an optimal policy can be interpreted as a random production run. Approximation techniques are presented for this case. The fixed production run model is an alternative technique for determining production lot sixes. The random production run model is an alternative to traditional Shewhart process control.

A Bayesian analogue of the Shewhart X-bar chart is defined and compared with cumulative sum charts. The comparison identifies types of production process where the Bayesian chart has better expected performance than the cumulative sum chart. Implementing the Bayesian chart requires more detailed knowledge of the process structure than is required by the best-known types of charts, but acquiring this information can yield tangible benefits.

No abstract

No abstract