A Polynomial Algorithm for Computing the Optimal Repair Strategy in a System with Independent Component Failures

TL;DR

This paper presents a polynomial time algorithm for determining the optimal repair strategy in systems with independent component failures, under specific behavioral restrictions, and extends it to hierarchical systems with inspection capabilities.

Contribution

It introduces a polynomial algorithm for optimal repair in systems with independent failures and extends it to hierarchical systems with inspection, addressing intractability in general cases.

Findings

Polynomial algorithm for optimal repair strategy in systems with independent failures

Linear time algorithm for hierarchical systems with inspection

Effective repair strategies with low expected cost

Abstract

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.