An optimal mixed policy of inspection and burn-in and the optimal production quantity

Inspection and burn-in are two techniques that are widely used by the vendor to screen out defective items in a production lot in order that an outgoing batch satisfies the purchaser's quality requirements. Due to two types of inspection errors and high cost of burn-in, how to make a trade-off between them is a challenge for the vendor. The main purpose of this paper is to deal with the problem of determining the optimal mixed policy of inspection and burn-in, where the average outgoing quality (AOQ) is used as a measure of inspection and burn-in success. More specifically, under the constraint that the outgoing batch meets an AOQ requirement, the following issues are determined to maximize the expected profit that the vendor makes: (a) the total number of items that the vendor needs to produce, (b) the number of items for inspection, the number of items for burn-in, and the number of items that need neither inspection nor burn-in, and (c) the optimal burn-in time if burn-in test is needed. Finally, an example is provided to illustrate the proposed method.