Exact and heuristic approaches to detect failures in failed k-out-of-n systems

Abstract

This paper considers a k-out-of-n system that has just failed. There is an associated cost of testing each component. In addition, we have apriori information regarding the probabilities that a certain set of components is the reason for the failure. The goal is to identify the subset of components that have caused the failure with the minimum expected cost. In this work, we provide exact and approximate policies that detects components' states in a failed k-out-of-n system. We propose two integer programming (IP) formulations, two novel Markov decision process (MDP) based approaches, and two heuristic algorithms. We show the limitations of exact algorithms and effectiveness of proposed heuristic approaches on a set of randomly generated test instances. Despite longer CPU times, IP formulations are flexible in incorporating further restrictions such as test precedence relationships, if need be. Numerical results illustrate that dynamic programming for the proposed MDP model is the most effective exact method, solving up to 12 components within one hour. The heuristic algorithms' performances are presented against exact approaches for small to medium sized instances and against a lower bound for larger instances.