Failure detection for series systems when tests are unreliable

In this study, we consider a failed series system in which any of the components of the system can be the cause of the failure with different probabilities. We sequentially test the components to detect the failed one by applying costly tests. Prior probability that a component is the cause of the failure as well as the cost of testing a component are known. We consider unreliable tests that can identify a component as working when in reality it is down, and vice versa. In addition to testing costs, there are costs corresponding to misclassification of the state of the system and the total expected cost becomes the sum of testing and misclassification costs. In this study, we propose a new model in which the repetition of tests are allowed. Therefore, the aim here is not only to determine the best test sequence, but also the best repetition strategy that provides the total minimum expected cost. We show how to compute the expected cost of such a given strategy. Heuristic algorithms are proposed to find good strategies for large problem instances. Numerical results are presented to demonstrate the possible cost reductions through repetition of the tests.