A polynomial algorithm for computing the optimal repair strategy in a system with independent component failures

The goal of diagnosis is to compute good re­ pair strategies in response to anomalous sys­ tem behavior. In a decision theoretic frame­ work, a good repair strategy has low expected cost. In a general formulation of the problem, the computation of the optimal (lowest ex­ pected cost) repair strategy for a system with multiple faults is intractable. In this paper, we consider an interesting and natural re­ striction on the behavior of the system being diagnosed: (a) the system exhibits faulty be­ havior if and only if one or more components is malfunctioning. (b) The failures of the sys­ tem components are independent. Given this restriction on system behavior, we develop a polynomial time algorithm for computing the optimal repair strategy. We then go on to in­ troduce a system hierarchy and the notion of inspecting (testing) components before re­ pair. We develop a linear time algorithm for computing an optimal repair strategy for the hierarchical system which includes both re­ pair and inspection.