An optimal inspection and replacement policy for a deteriorating system

Abstract

This paper investigates a system whose deterioration is expressed as a continuous-time Markov process. It is assumed that the state of the system cannot be identified without inspection. This paper derives an optimal policy minimizing the expected total long-run average cost per unit time. It gives the optimal time interval between successive inspections and determines the states at which the system is to be replaced. Furthermore, under some reasonable assumptions reflecting the practical meaning of the deterioration, it is shown that the optimal policy has monotonic properties. A control limit rule holds for replacement, and the time interval between successive inspections decreases as the degree of deterioration increases.

Maintenance optimization for a Markovian deteriorating system with population heterogeneity

“…Many engineering systems are subject to both gradual deterioration and random shocks that cause sudden failures (Lam and Yeh, 1994). In a continuous-time setting, researchers have modeled such deterioration processes as a continuous-time Markov chain in which, from any deterioration level, transitions can be made to the next-higher deterioration level or to the failed state (Ohnishi et al, 1986;Lam and Yeh, 1994;Chiang and Yuan, 2001). In discrete time, if the deterioration level is monitored at sufficiently small time intervals and gradual deterioration is a process with stationary increments, such deterioration behavior can be captured by a transition probability matrix of the form…”

Méthode asymptotique pour l’estimation des paramètres d’un système multi-états soumis à une maintenance conditionnelle

“…In the scientific litterature, many authors proposed degradation and lifetime models to assess and optimize condition-based maintenance policies (see the survey [Wang, 2002]). [Mine et al, 1975] and [Ohnishi et al, 1986] considered a continuous time but discrete state semi-Markov deterioration process, whereas [Park, 1988], [Barbera et al, 1996], and [Wang et al, 2000] dealt with continuous wear processes. In [Van Noortwijk, 2009] and [Deloux et al, 2009], the authors modeled the deterioration by a gamma process.…”

Optimal condition-based maintenance policy for a partially observable system with two sampling intervals

“…Recently, [18] has formulated and analyzed this joint optimization problem in a discrete setting and established the form of the optimal policy. An early work which demonstrates the benefits of non-periodic sampling of a deteriorating system with N fully observable states is [22]. Under reasonable monotonicity assumptions, the authors partially characterized the form of the optimal policy and proved that the equidistance sampling is not optimal and the time between two consecutive samples should monotonically decrease as the system deteriorates.…”