When a unit repeats some works over again and undergoes minimal repairs at failures, it is more practical to replace it preventively at the end of working cycles or at its failure times. In this case, it would be an interesting problem to know which is better to replace the unit at a number of working cycles or at random failures from the point of cost. For this purpose, we give models of the expected cost rates for the following replacement policies: (1) The unit is replaced at a working cycle N and at a failure number K, respectively; (2) Replacement first and last policies with working cycle N and failure number K, respectively; (3) Replacement overtime policies with working cycle N and failure number K, respectively. Optimizations and comparisons of the policies for N and K are made analytically and numerically.

The maintenance of a system on a ship has limitations when the ship is engaged in a voyage because of limited maintenance resources. When a system fails, it is either repaired instantly on ship with probability p or remains unrepaired during the voyage with probability 1-p owing to the lack of maintenance resources. In the latter case, the system is repaired after the voyage. We propose two management policies for the overhaul interval of an IFR system: one manages the overhaul interval by number of voyages and the other manages it by the total voyage time. Our goal is to determine the optimal policy that ensures the required availability of the system and minimizes the expected cost rate.

A one-shot system is a system that can be used only once during its life, and whose failures are detected only through inspections. In this paper, we discuss an inspection policy problem of one-shot system composed of multi-unit in series. Failed units are minimally repaired when failures are detected and all units in the system are replaced when the nth failure is detected after the last replacement. We derive the expected cost rate approximately. Our goal is to determine the optimal inspection policy that minimizes the expected cost rate.

This paper considers replacement and maintenance policies for an operating unit which works at random times for jobs. The unit undergoes minimal repairs at failures and is replaced at a planned time T or at a number N of working times, whichever occurs first. The expected cost rate is obtained, and an optimal policy which minimizes it is derived analytically. The imperfect preventive maintenance (PM) model, where the unit is improved by PM after the completion of each working time, is analyzed. Furthermore, when the work of a job incurs some damage to the unit, the replacement model with number N is proposed. The expected cost rate is obtained by using theory of cumulative processes. Two modified models, where the unit is replaced at number N or at the first completion of the working time over time T, and it is replaced at T or number N, whichever occurs last, are also proposed. Finally, when the unit is replaced at time T, number N or Kth failure, whichever occurs first, the expected cost rate is also obtained.

Burn-in is a widely used method to improve the quality of products or systems after they have been produced. In this paper, optimal burn-in procedures for a system with two types of failures (i.e., minor and catastrophic failures) are investigated. A new system surviving burn-in time b is put into field operation and the system is used under a warranty policy under which the manufacturer agrees to provide a replacement system for any system that fails to achieve a lifetime of at least w. Upper bounds for optimal burn-in time minimizing the total expected warranty cost are obtained under a more general assumption on the shape of the failure rate function which includes the bathtub shaped failure rate function as a special case.