Optimal inspection and repair of renewable coherent systems with independent components and constant failure rates

Suppose that a multicomponent reliability system earns revenue while it is working and that it has a finite number of possible failure states (defined as states in which it ceases to work), each with a known prior probability. When the system stops working its components can be inspected one at a time, and, if necessary, replaced or repaired, until the system is restored to its original (operating) state. Inspections (as well as replacements or repairs) are time consuming and expensive. An optimal adaptive inspection strategy for examining and fixing the components of a failed system restores it as efficiently as possible, taking into account the opportunity costs due to lost revenue while the system remains failed as well as the costs and times required for inspections. This article presents exact and heuristic procedures for constructing optimal adaptive strategies for k-out-of-n and general coherent systems. Average revenue per unit time is taken as the maximand for most of the article, but characterizations of optimality are also obtained for series systems in the case of discounted return over an infinite planning horizon.