The generalized age maintenance policies with random working times

The purpose of this paper is to investigate the generalized age maintenance policies for a system with random working times. When the system fails, it is subject to one of two types of failures with age-dependent probability: type I failure can be removed by minimal repair and type II failure must be rectified by replacement. First, the system is preventively replaced before type II failure at time T or at the completion of Nth working projects, whichever occurs first. Two modified models, where the system is preventively replaced before type II failure at time T or at the completion of Nth working projects, whichever occurs last, and it is preventively replaced at the first completion of the working project over time T or at the completion of Nth working projects, whichever occurs first, are considered. By introducing costs due to repairs, maintenance and replacement, the expected cost per unit time is derived as a criterion of optimality and the optimal policy that minimizes that cost is discussed analytically.