This study presents an extended replacement policy for a two-unit system which is subjected to shocks and exhibits failure rate from interaction. The external shocks that affect the system are of two types. A type I shock causes a minor failure of unit-A and the damage that is caused by such a failure affects unit-B, whereas a type II shock causes a total failure of the system (catastrophic failure). All unit-A failures can be recovered by making minimal repairs. The system also exhibits the interaction between the failure rates of units: a failure of any unit-A causes an internal shock that increases the failure rate of unit-B, whereas a failure of a unit-B causes instantaneous failure of unit-A. The goal of this study is to derive the long-run cost per unit time of replacement by introducing relative costs as a factor in determining optimality; then, the optimal replacement period, T*, and the optimal number of unit-A failures, n*, which minimise that cost can be determined. A numerical example illustrates the method.

A retrial queue with constant retrial policy, unreliable servers and the failed servers may not be detected is investigated in this paper. Upon arrival, a customer either is attended to one of the available servers or enters a retrial orbit and retries in a random time as all servers are not available. The unreliable server can be breakdown when he is working. The breakdown server may not be detected due to some fault matters. Under such a situation, the repair facility will issue a reboot operation to locate the non-detected breakdown server. Once the breakdown server is detected and located, he will be sent for repair. After utilizing the general theory of matrix-geometric approach to determine the stationary distribution, some performance measures are proposed. A single-objective model aiming at minimizing the average cost is constructed. We apply particle swarm optimization algorithm and genetic algorithm to find the optimum combination of parameters. We also formulate a bi-objective model aiming at minimizing the expect cost and the mean waiting time of customers in orbit. Two multi-objective algorithms are developed to solve it.

We consider a system consisting of two units (A and B), which is subject to two types of shocks (I and II) that occur according to a non-homogeneous Poisson process. The probabilities of these two shock types are age-dependent. Each type-I shock causes a minor failure of unit A, which can be corrected by a minimal repair. Meanwhile, this type of shock results in a certain amount of damage to unit B. These damages to unit B are accumulated to trigger a preventive replacement (PM) or a corrective replacement (CM) action. In addition, a minor failure for unit B with the cumulative damage of z will occur with probability at a type-I shock instant. Type-II shock is a major one that causes system replacement. We consider a two-dimensional PM policy, which prescribes that the system is preventively replaced at age T, or at the time when the total damage to unit B exceeds a prespecified level Z (but less than the failure level K where K > Z) or is replaced correctively at first type-II shock or when the total damage to unit B exceeds a failure level K, whichever occurs first. Thus, both PM and CM actions may be performed in our model. To minimise the expected cost per unit time, the optimal policy ( , ) is derived analytically and determined numerically. We also show that our model is a generalisation of many previous maintenance models in the literature.