基于时间区间型的随机维修策略研究

The random maintenance policies, mainly involving preventive replacement models for exponential failure times and preventive maintenance models for random mission times, have great theoretical and practical significance in reliability theory. However, to the best of our knowledge, there hasn’t been much research on random maintenance policies and their applications at home and abroad. The most problem of a random maintenance policy is that it pays the cost of reliability for running missions successively, where the mission times are supposed to be random variables. In order to resolve this problem, we firstly study the failure rates and their mathematical properties for random replacement models, and then, we optimize the upper and lower bounds of an time interval, during which the random replacement policy is performed, and the constantly planned replacement policy is performed at time of the upper bound. We are going to survey the application of the random maintenance models into a T/R module system for a Phased Array Radar when it runs for successive missions. It will be shown that, when the T/R module system is considered as a random and repairable k-out-of-n system, our new imperfect maintenance policy with an optimum time interval will increase the reliability of the system and then save the expected cost rate of maintenance. The modeling approaches contributed in this project will offer some inspirations for researchers and some practical ways for engineers, who are now engaging in works in areas of reliability and maintainability.

随机维修策略解决了包括预防更换模型在指数型失效分布下的理论求解问题，并且满足了系统执行连续性随机任务的维修工程需求，具有较大的理论与应用价值。然而，随机维修策略的相关理论研究与实践应用在国内外并不多见。为解决随机维修策略由于可执行需求而带来的可靠性或经济性问题，本项目首先研究随机更换模型的失效率函数及其数学性质，进而重点研究基于时间区间型的随机更换策略的模型构建方法。结合有源相控阵雷达天线阵面的维修设计理念，我们抽象其收发组件系统为随机表决系统，为进一步避免维修资源的浪费问题，本项目最后利用时间区间型建模方法讨论面向连续性任务的随机表决系统的不完全预防维修策略。通过本项目的研究，我们能更深刻地掌握随机维修策略在可靠性与可执行性方面的适用性，为解决维修工程问题提供新的理论与方法支撑。

随机维修策略解决了包括预防更换模型在指数型失效分布下的理论求解问题，并且满足了系统执行连续性随机任务的维修工程需求，具有较大的理论与应用价值。..随机维修策略的相关理论研究与实践应用在国内外并不多见。为掌握随机维修策略在可靠性与可执行性方面的实施方法，为解决维修工程问题提供新的理论与方法支撑，本项目主要研究了：预防超额与事后短缺成本的描述方法；预防更换模型的失效率函数的构建方法；基于时间区间型的随机更换策略的建模方法；多变量随机更换策略的建模方法；随机表决系统的预防维修策略的建模方法。..本项目从可靠性与可执行性的角度建立随机维修模型，而非只局限于根据系统失效规律或健康状态来研究预防更换策略或预防维修策略，其可执行性需求体现于策略提出阶段，其可靠性需求则体现于模型讨论过程中对失效率函数的研究。本项目研究的特色也在于：通过数学解析的方法构建与讨论随机维修策略模型，模型与解析结果具有理论研究的延续性价值。