The optimal production and quality policy for the vendor in a trade

Arranging an inspection schedule for the production process and taking inspection and burn-in tests to screen out defective items in a production lot before items are shipped to the buyer are widely used by the vendor, such that the defective percentage in an outgoing batch satisfies the quality requirement specified in the contract between them. For an inspection schedule, the number of inspections and the length of time intervals between two inspections are influential to both the precision of detecting the manufacturing process and the inspection cost. As to the inspection test, it is not perfect, so there are two types of errors (Types I and II). Nevertheless, compared with inspection test, burn-in is usually costly. Hence, how to make a suitable trade-off between these three treatments (i.e., inspection schedule, inspection test, and burn-in test) such that the outgoing batch satisfies the purchaser's quality requirement with low cost is an important issue. The main purpose of this paper is to deal with the problem of determining the optimal inspection schedule and the optimal mixed policy of inspection and burn-in, where the average outgoing quality is used as the measure of quality. More specifically, by using the criterion of maximizing the expected profit that the vendor makes in a trade, a nonlinear programming problem is built to determine (a) the number of inspections undertaken in the production process, (b) the times at which the production process is inspected, (c) the total number of items that the vendor should produce (or the production run time), (d) the number of items for inspection, the number of items for burn-in, and the number of items that need neither inspection or burn-in, and (e) the optimal burn-in time for those needing burn-in testing. An example is provided to illustrate the proposed method.