@article{ref1,
title="Optimal replacement in a proportional hazards model with cumulative and dependent risks",
journal="Computers and industrial engineering",
year="2023",
author="Zhou, Huaxiang and Li, Yizhu",
volume="176",
number="",
pages="e108930-e108930",
abstract="This paper deals with a new maintenance problem with two competing dependent risks: minor failures and major failures. The cumulative number of minor failures is incorporated into the proportional hazards model as a covariant process of the hazard function of major failures. We introduce the &quot;Time Discrete Markovian Approximation&quot; (TDMA) technique to solve the &quot;curse of dimensionality&quot; in Markov Decision Processes (MDP) and simplify the high-dimensional integration when computing the average cost by renewal theory. We develop a new optimal control limit policy with a &quot;mixed hazards function&quot; as the threshold and reveal its agreement with the solution from MDP. Additionally, a corresponding iterative algorithm is developed to produce a sequence converging to the optimal solution faster than the policy iteration.<p /> <p>Language: en</p>",
language="en",
issn="0360-8352",
doi="10.1016/j.cie.2022.108930",
url="http://dx.doi.org/10.1016/j.cie.2022.108930"
}