ABSTRACT

This paper considers a periodic preventive maintenance policy for a deteriorating and repairable system. The system is subject to random failures and is repaired at each failure. To improve the reliability, at periodic times iT (i = 1, 2, … N–1), the system is preventively maintained (PM). At the time NT the system is replaced. The failure/repair process between two PMs follows the Non-Homogeneous Pure Birth Process (NHPBP) which is a generalized version of the Non-homogeneous Poisson process (NHPP). The reliability improvement made by a PM action is stochastically modeled based on the properties of NHPBP. The cost for each PM depends on the reliability condition of the system at that PM time. The PM policy is characterized by the two parameters (N, T). We develop a two-stage procedure to find the optimal (N*, T*) which minimizes the long-run expected cost rate. Numerical examples are presented to illustrate the properties of the optimal policies.

Abbreviations: NHPBP: Non-homogeneous pure birth process; NHPP: Non-homogeneous Poisson process; PM: Preventive maintenance; CM: Corrective maintenance; RM: Replacement maintenance

摘要

本文考虑了恶化和可修复系统的定期预防性维护策略。该系统会遭受随机故障的影响，并且每次发生故障时都会对其进行维修。为了提高可靠性，在周期性时间iT（i = 1，2，… N –1）上，系统要进行预防性维护（PM）。当时的新台币系统已更换。两个PM之间的故障/修复过程遵循非均匀纯生过程（NHPBP），这是非均匀泊松过程（NHPP）的通用版本。基于NHPBP的特性，随机模拟了PM动作所带来的可靠性提高。每个PM的成本取决于该PM时系统的可靠性状况。PM策略的特征在于两个参数（N，T）。我们开发了一个两阶段的程序来找到最佳的（N *，T *），以最小化长期预期成本率。数值例子说明了最优策略的性质。

缩写：NHPBP：非均一的纯出生过程；NHPP：非均匀泊松过程；PM：预防性维护；CM：纠正性维护；RM：更换维护