Optimal Scheduling of Inspections: A Delayed Markov Model with False Positives and Negatives

A system subject to catastrophic failure deteriorates according to a delayed Markov process and is subjected to a series of binary tests that may yield false negative and false positive outcomes. A corrective action is carried out when a true positive is observed, thereby reducing the chance of system failure. Costs of inspections, false positives, the corrective action, and failure are incurred, and dynamic programming is used to compute the optimal inspection schedule. Two tractable computational methods are developed. The model, which is suited for medical screening, is applied to the problems of post-operative periumbilical pruritis and breast cancer.