具有预防维修的多状态退化系统的维修替换策略分析

In maintenance problem, it is often to assume that a failed system after repair will be `as good as new'. However, most systems are deteriorating because of the ageing effect and the accumulated wearing. Therefore, the study of the optimal maintenance and replacement policy for deteriorating systems have great theoretical and practical significance. Preventive repair is very valid method of maintenance. So,the multistates deteriorating systems with preventive repair are analyzed. Based on the theory of geometric process, a few of deteriorating system models of a single unit system and series system are established. It is assumed that the work will be interrupted and the preventive repair will be executed as soon as the system reliability reaches to an determined constant or undetermined constant. Failure repair is excuted as soon as the system fails. The system will be replaced when the number of failures of the system reaches to N. The successive operating times after repair form a decreasing geometric process, while the consecutive repair times after failure form an increasing geometric process. Using renewal process theory, the explicit expression of the long-run expected cost per unit time of the system is derived. The optimal maintenance and replacement policies which minimize the long-run expected cost per unit time of the system are given analytically and numerically. Some comparisons and analysis with existing policies are also discussed by numerical methods. It has some theorial significance to guide enterprises to reasonable use and maintenance eqipments, reduce production costs, enhance economic efficiency and security of the system.

在维修问题中，经常假设故障系统的维修是"修复如新"的，然而由于年龄的影响和磨损的积累，大多数系统都是退化的，因此研究退化系统的最优维修替换策略问题具有重要的理论和实际意义。采用预防维修是非常有效的维护手段,因此本课题研究带有预防维修策略的多状态退化系统模型,以几何过程理论为基础,建立各种单部件和串联退化系统模型,假设在故障前，采用等长的和变长的预防维修策略，在故障后采用故障维修，并结合替换策略N，当系统故障维修了N次不再进行修理，而是替换上全新系统；假设系统修理后相继的工作时间形成了单调递减的几何过程，而相继的修理时间形成了单调递增的几何过程。根据更新过程理论，推导出系统长期运行单位时间的平均费用表达式，并分析地和数值地给出最优替换策略，并与现有的策略进行数值地比较和分析。这些理论的计算，对于指导企业合理使用及维护设备、降低生产成本、提高经济效益和系统安全性均具有一定的指导意义和参考价值。

基于几何过程理论，讨论退化系统的维修替换策略问题，这是目前可靠性理论研究中的一个热门话题。多状态系统是一类重要的可靠性模型，为了提高系统的可靠度避免故障的发生，经常会采取必要的预防维修策略。本项目就对带有预防维修的多状态退化系统的维修替换策略进行了深入研究。（1）首先我们研究了单部件三状态系统的维修策略问题，当系统的失效率达到一个固定的值时，就对系统进行预防维修，并在故障后采用故障维修，推导出系统长期运行单位时间的平均费用，数值地给出最优替换策略。并与定期预防维修策略和基于可靠度的预防维修策略进行比较分析，得出基于失效率的预防维修策略更优的结果；（2）接下来研究了单部件多状态系统的维修替换策略问题，采用基于可靠度的预防维修策略，当系统的可靠度下降到一定水平，就进行预防维修，根据更新过程理论，推导出系统长期运行的单位时间的平均费用表达式，并数值地给出了最优替换策略，而且分析地得到此模型与带有预防维修的两个状态几何过程模型的等价关系；（3）然后又将部件推广到多部件退化系统中，先研究了不带预防维修的多部件串联的多状态退化系统的维修替换策略分析。系统由多个不同部件串联而成，每个部件具有多个故障状态，部件故障后立即进行维修，不能修复如新。采用替换策略M，部件i第Ni次故障后不再修理，而是替换上全新的部件。在替换策略M下，推导出了系统长期运行单位时间的平均费用表达式。(2)研究了带有预防维修的多状态退化系统，对于每个部件i，当可靠度降到一定水平时，就进行预防维修，当部件i故障后立即进行维修，不能修复如新。推导出了系统长期运行单位时间的平均费用表达式。