The optimal frequency and sequencing of tests in the inspection of multi-characteristic components

A product (component) often requires inspection on its characteristics, of which nonconformance of one would result in the rejection of the component. However, the need for inspection should also be justified in terms of the costs involved. Because the defective rates, the testing errors (Types I and II), and the inspection costs are different across characteristics, not all the tests are cost effective to be conducted, whereas some of them may be justified in being executed more than once. What tests should be selected? How many times should a test be conducted? In what sequence should selected tests be carried out? On the basis of the theorems established in this paper, an efficient algorithm for finding the optimal inspection plan is developed. An example problem is solved and the results are studied. Finally, some extensions of the model are discussed.