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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,

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.

Increasingly, real-time systems are being used in applications that contain tasks that have deadlines and require predictable performance. Many complex real-time applications require modern operating systems capable of scheduling multiple classes of tasks in an integrated way. These applications require scheduling that result in high utilization of available processing power to accommodate as many tasks as possible while satisfying the required deadlines of each task. In this paper, we propose a combined heuristic approach to schedule a set of independent soft and hard real-time tasks in multiprocessor computing systems. Each of these tasks is characterized by its arrival time, deadline and required processing power. The proposed approach distributes the total available processing power of any processor, if it is needed and possible, among more than one task, while ensuring that hard real-time tasks are given higher priority and enough processing power to meet deadlines. This strategy can be used as a tool to efficiently guide scheduling processes. In addition, it can help to optimize processor utilization and maintain higher success ratios by maximizing the schedulability of soft tasks without jeopardizing the schedulability of hard tasks.