Optimal Maintenance/Replacement-Policy for Deteriorating Systems under Two-Phase Maintenance Strategy

Abstract

In this paper, a maintenance strategy is proposed for a multi-state deteriorating system subject to both aging and fatal shocks under continuous inspection. The strategy allows one of the three actions "do nothing", "maintenance" or "replacement" to be taken at each state of the system. A two-phase maintenance is applied and an optimal state-dependent maintenance/replacement policy for the system is derived. At each state, only a given number of successive minimal repairs can be performed, which is followed by one minimal maintenance. The overall number of allowable minimal maintenances for all states may not exceed a given limit. An iteration algorithm is used for determining the optimal policy, which minimizes the long-run cost per time of the system. Numerical examples are given to illustrate and evaluate the performance of the proposed policy.

Optimal control limit policy for age-dependent deteriorating systems under incomplete observations

“…As presented in previous research, 2,3,6,12 the control limit policy can substantially reduce computational effort by simplifying the algorithm and reducing computation errors. This means that the tremendous amount of calculation time required to find the optimal maintenance policy is reduced if the optimal maintenance policy can be limited to the set of control limit policies.…”

“…Complete Incomplete State Derman, 1 Lam and Yeh, 2 Monahan, 7 Smallwood and Sondik, 8 Moustafa and Maksoud, 3 Grosfeld-Nir, 9 Ohnishi et al, 10 Lovejoy, 11 Douer and Yechiali, 4 Kurt and Kharoufeh, 5 Maillart, 12 Maehara and Suzuki, 13 Elwany et al 6 Jin et al, 14 Zouch et al 15…”

“…In the classic stationary MDP model for complete observations, the control limit policy may be viewed as bisections of the one-dimensional system state space. 1–6 In the models of incomplete observations, the decision is made on the basis of a state information vector, and a control limit policy is investigated on a statistical ordered set. 9–14 In almost all works, the deterioration of a system is considered to depend only on its state, and the proposed control limit policy is a state-dependent control limit policy.…”

“…The replacement problem is formulated as an MDP and the optimal replacement policy is shown to be a control limit policy. Complete observation in previous research means that the true state of a Department of Informatics, University of Electro-Communications, Japan system can be known exactly, [1][2][3][4][5] or that the observation fully captures the underlying deterioration state of the system being observed. 6 However, in many cases, the monitoring system can only provide incomplete information related to the true state since it suffers from false alarm and failure to alarm.…”

“…Extensive investigation of Lam and Yeh’s 2 research can be found in Moustafa and Maksoud. 3 Douer and Yechiali 4 proposed a generalized control limit policy for the optimal repair and replacement of Markov deteriorating systems under the total expected discounted cost and long-run average cost criteria. Kurt and Kharoufeh 5 extended Derman’s 1 model to a general deteriorating system in a controllable environment and obtained sufficient conditions for the optimality of a control limit policy.…”