The finite-time-period preventive maintenance policies with failure rate reduction under a warranty consideration

In practice, a system or equipment has a finite useful life. When an aged system is replaced by a new system, the new system seldom has exactly the same characteristics, functions, investment cost, maintenance expenses, etc., as those of the aged system. However, the literature has shown that most researchers are devoted to studying maintenance problems in an infinite time span, which assumes that the replaced system in each replacement cycle (or period) has the same conditions and costs. Apparently, the assumption might not be practical, since the useful operating life of most systems is finite in the real world. Therefore, the purpose of this research is to develop an optimal preventive maintenance (PM) policy having failure rate reduction within a finite time span under a warranty consideration by minimizing the expected total maintenance cost. The PM cost is assumed to be a linear function of each PM effect. Two cases are studied and compared; one is with no warranty provided and the other is with a given warranty period. For the second case, we examine two policies: (1) no PM within the warranty period is assumed and (2) the PM will be performed within the warranty period. In this article, the algorithm for searching the optimal solution is presented. Examples with Weibull failure cases are given and the sensitivity analysis of the optimal solution is also provided.