Economic design of multiple inspection plans via the expectation-maximization algorithm

Because of inspection errors, expensive items such as computer chips are usually inspected more than once with the same testing device to further improve the quality of accepted items. Many researchers have considered various multiple inspection plans that minimize the expected total cost of inspection and misclassifications. We first propose a new Markovian inspection plan under which each item is tested repeatedly until we have a sufficient number of positive or negative test results. We then deal with the problem of estimating three model parameters: the type I and II errors of an automated test equipment and the fraction defective of incoming items. Because of computational difficulties in maximizing the likelihood of the three parameters, we propose the use of the expectation-maximization (EM) algorithm as an easy alternative. In a numerical analysis, we demonstrate the outstanding performance of our new inspection plan over previous ones.