A Polynomial Algorithm for Computing the Optimal Repair Strategy in a System with Independent Component Failures
This addresses the challenge of efficient diagnosis and repair in systems like engineering or computing, offering practical solutions for maintenance tasks, though it is incremental as it builds on known restrictions.
The paper tackles the problem of computing optimal repair strategies for systems with independent component failures, which is generally intractable, and develops a polynomial-time algorithm to find the lowest expected cost strategy. It also extends this to hierarchical systems with inspection, providing a linear-time algorithm for optimal strategies.
The goal of diagnosis is to compute good repair strategies in response to anomalous system behavior. In a decision theoretic framework, a good repair strategy has low expected cost. In a general formulation of the problem, the computation of the optimal (lowest expected cost) repair strategy for a system with multiple faults is intractable. In this paper, we consider an interesting and natural restriction on the behavior of the system being diagnosed: (a) the system exhibits faulty behavior if and only if one or more components is malfunctioning. (b) The failures of the system 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 introduce a system hierarchy and the notion of inspecting (testing) components before repair. We develop a linear time algorithm for computing an optimal repair strategy for the hierarchical system which includes both repair and inspection.