Publication Type

Journal Article

Version

acceptedVersion

Publication Date

9-2025

Abstract

Although most on-demand mission-critical systems are engineered to be reliable to support critical tasks, occasional failures may still occur during missions. To increase system survivability, a common practice is to abort the mission before an imminent failure. We consider optimal mission abort for a system whose deterioration follows a general three-state (normal, defective, failed) semi-Markov chain. The failure is assumed self-revealed, whereas the healthy and defective states have to be inferred from imperfect condition-monitoring data. Because of the non-Markovian process dynamics, optimal mission abort for this partially observable system is an intractable stopping problem. For a tractable solution, we introduce a novel tool of Erlang mixtures to approximate nonexponential sojourn times in the semi-Markov chain. This allows us to approximate the original process by a surrogate continuous-time Markov chain whose optimal control policy can be solved through a partially observable Markov decision process (POMDP). We show that the POMDP optimal policies converge almost surely to the optimal abort decision rules when the Erlang rate parameter diverges. This implies that the expected cost by adopting the POMDP solution converges to the optimal expected cost. Next, we provide comprehensive structural results on the optimal policy of the surrogate POMDP. Based on the results, we develop a modified point-based value iteration algorithm to numerically solve the surrogate POMDP. We further consider mission abort in a multitask setting where a system executes several tasks consecutively before a thorough inspection. Through a case study on an unmanned aerial vehicle, we demonstrate the capability of real-time implementation of our model, even when the condition-monitoring signals are generated with high frequency.

Keywords

Semi-Markov chain; partially observable Markov decision process; control-limit policy; mixture of Erlang distribution, optimal stopping

Discipline

Databases and Information Systems | Operations and Supply Chain Management

Research Areas

Integrative Research Areas

Publication

Operations Research

Volume

73

Issue

5

First Page

2396

Last Page

2416

ISSN

0030-364X

Identifier

10.1287/opre.2022.0643

Publisher

Institute for Operations Research and Management Sciences

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1287/opre.2022.0643

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