A semi-Markov decision algorithm for the optimal maintenance of a multistage deteriorating two-unit standby system

Abstract

The semi-Markov decision model is a powerful tool in analyzing sequential decision processes with random decision epochs for a multi-state deteriorating system subject to aging and fatal shocks. In this paper, we propose a model for a two-unit standby system where a cold standby unit is attached to an operating (active) one. For this model, the active unit goes through a finite number of states of successive degradation preceding the failure, while the other one is in cold standby state. At each deterioration state of the active unit, two types of maintenance are considered, minimal and major, depending on the degrading level. The minimal maintenance aims to improve the degradation of the unit by recovering it to the previous degradation stage. The maximum allowable number of minimal maintenances for all states of the active unit must not exceed a certain limit. On the other hand, the major maintenance is necessary when the active unit fails. Once this maintenance is completed, the unit is restored to as good as new. To make the system operate more time without any interruption, the standby unit can be switched online until the active unit finishes its minimal or major maintenance. The switch between the two units is perfect and switchover is instantaneous. After using the standby unit, it is serviced or overhauled to maintain it in as good as new state. We use an iterative numerical approach, based on the policy iteration method, to drive the optimal state-dependent maintenance policy that minimizes the long-run expected cost rate of the system. Finally,

Optimal maintenance service outsourcing strategy considering extended warranty service

“…Some scholars pay attention to the content of the maintenance service. For instance, Maksoud and Moustafa (2009) drive the optimal state‐dependent maintenance policy through a semi‐Markov decision model. They consider two types of maintenance, minimal and major.…”

Reliability-redundancy allocation Problem of a queueing system considering energy consumption

“…Due to the complexity of the RRAP, most of the researches has focused on developing heuristic and metaheuristic approaches. In this regard, we can refer to Simulated Annealing (SA) [8], Genetic Algorithm (GA) [4,[9][10][11][12], Particle Swarm Optimization (PSO) [5,6,[13][14][15][16], Artificial bee colony algorithm [3,17], Artificial immune search [18], Biogeography-based optimization (BBO) [19], fruit fly optimization algorithm [20], Markov decision process [21], Stochastic Fractal Search (SFS) [22], and hybrid algorithms such as SFS-GA [23]. In addition to heuristic and metaheuristic algorithms, simulation-based solution approaches [24] and exact solution methods such as implicit enumeration, branch-and-bound, and dynamic programming have also been used to solve RRAP [23].…”

An optimal maintenance strategy for multi-state systems based on a system linear integral equation and dynamic programming

“…Additional information on reliability analyses and maintenance strategies for MSSs based on Markov or semi-Markov processes can be found in other research works (cf. [6,10,17,19,23,24,25,41]).…”

“…Many models and strategies treat minimization of the expected long-run cost per unit time as the objective function when designing an optimal maintenance strategy (cf. [23,30,35,36,40]). However, many realistic repairable systems including productive systems, control systems and chemical systems often result in devastation when they fail.…”

“…The determination of W is described in [23]. To validate the wide applicability of the proposed optimal strategy, two different types of distribution, i.e., a Weibull distribution and a more general distribution, are considered in cases 1 and 2, respectively.…”