修理工单重定期休假可修系统更换模型研究

针对修理工带有单重休假的单部件可修系统,提出了一种新的维修更换模型.假定系统是可修的,逐次故障后的维修时间构成随机递增的几何过程,系统工作时间构成随机递增的几何过程,在修理工休假时间为定长的情况下,分别选取系统的总工作时间T和故障维修次数N为更换策略,以长期运行单位时间内的期望效益为目标函数,通过更新过程和几何过程理论建立数学模型,导出了目标函数的解析表达式,通过最大化目标函数来获取系统最优的更换策略T*和N*.并在一定条件下给出了策略N比策略T优的充分条件.最后,通过数值例子验证了方法的有效性.     

修理工可单重休假的预防维修更换策略

本文研究了一个修理工带有单重休假的单部件可修系统.为了延长系统的使用寿命,在系统故障前考虑了预防维修,且假定预防维修能够“修复如新”,而故障维修为“修复非新”时,以系统的故障次数N为更换策略.通过更新过程和几何过程理论,得出系统经长期运行单位时间内期望费用的明显表达式,并对预防维修的定长间隔时间T及更换策略N进行了讨论,最后,通过实例分析,求出最优策略N’,使得目标函数取得最优值.     

有采购提前期的两部件串联系统的更换策略

研究了由两个不同型部件组成的串联系统的最优更换策略,当部件需要更换时,新的同型部件需要提前订购.当部件发生故障时对其进行维修,维修后的工作时间形成随机递减的几何过程,且每次故障后的修理时间形成随机递增的几何过程.以部件更换前的故障次数(N_1,N_2)为策略,以系统经长期运行单位时间内的期望费用最小为目标,研究了二维最优策略问题,给出了寻找最优策略的方法和数值分析.     

延误休假且修理延迟的可修系统的更换策略

研究了修理工多重延误休假且修理延迟的可修系统,假设系统故障后均不能"修复如新",系统在准备休假期间故障的概率为q,系统延迟修理的概率为1-P,以系统故障次数为更换策略,运用更新过程和几何过程理论,得出系统长期运行单位时间内平均停机时间的表达式,并通过数值例子验证了存在最优策略,使得平均停机时间最短.     

基于修理设备的冷贮备可修系统的维修策略

本文研究了两同型部件,一个修理设备组成的冷贮备可修系统.在故障部件不能"修复如新"的条件下,分别以系统中部件1故障次数N,工作时间T和(N,T)为维修策略,利用更新过程和几何过程,求出修理设备经长期运行单位时间内平均停工时间表达式.并在部件寿命的分布函数和修理时间的分布函数已知的情况下,以部件1故障次数N为策略证明存在最优N*使修理设备经长期运行单位时间内平均停工时间最长.最后,通过数值例子验证最优策略的存在性.     

带有多重休假及预防维修的冲击模型二维更换策略

研究了修理工带有多重休假且定期检测的累积冲击模型.为了延长系统的运行时间,在检测时考虑了预防维修.将事后维修和预防维修结合起来运用于可修系统,且假定预防维修能够"修复如新",而事后维修为"修复非新".以系统的检测周期和故障次数为二维决策变量,选取系统经长期运行单位时间内期望费用为目标函数.并通过数值分析,求出了最优策略.     

基于故障率减少的不完全维修模型

针对可修系统在实际的运行过程中无法通过维修手段恢复如新的情况,通过考虑维修后故障率的直接减少建立了可修系统的不完全维修模型,以此描述可修系统维修改善的效果.在不完全维修模型的基础上,构建了系统的成本函数,得到了系统最优的预防性维修次数和预防性维修时间间隔.最后,通过实例验证了模型的可行性和有效性.     

泊松冲击下阈值为几何过程的可修系统的最优更换策略（英文）

本文研究泊松冲击下的单部件可修系统,假设系统并非"修复如新".系统失效有可能由于外部冲击或者内部因素引起,并且冲击到达服从一个泊松过程.当冲击量大于系统的预先定好的一个阈值,则系统就会失效.假设系统在维修以后相邻之间的阈值形成一个几何过程,而系统的修理时间服从α-幂过程.利用更新过程理论,求出系统经长期运行单位时间内的期望损失及相应的最优更换策略.最终通过数值案例验证了模型中的结果.     

计及预防维修时间的一个故障维修模型

本文研究了单部件一个修理工组成的可修系统，为延长其使用寿命，在故障前考虑了预防维修，且假定预防维修能“修复如新”，而故障维修为“修复非新”时，利用几何过程，以系统２次数Ｎ为更换策略，选择最优的Ｎ，使得系统经长期运行单位时间的期望费用最小，最后，还对预防维修的定长间隔时间及更换策略进行了讨论。     

有延迟修理的两部件串联系统的预防维修策略

研究由两个部件串联组成的系统的预防维修策略, 当系统的工作时间达到T时进行预防维修, 预防维修使部件恢复到上一次故障维修后的状态. 当部件发生故障后进行故障维修, 因为各种原因可能会延迟修理. 部件在每次故障维修后的工作时间形成随机递减的几何过程, 且每次故障后的维修时间形成随机递增的几何过程. 以部件进行预防维修的间隔T和更换前的故障次数N组成的二维策略(T,N)为策略, 利用更新过程和几何过程理论求出了系统经长期运行单位时间内期望费用的表达式, 并给出了具体例子和数值分析.     

A novel optimal preventive maintenance policy for a cold standby system based on semi-Markov theory

A novel optimal preventive maintenance policy for a cold standby system consisting of two components and a repairman is described herein. The repairman is to be responsible for repairing either failed component and maintaining the working components under certain guidelines. To model the operational process of the system, some reasonable assumptions are made and all times involved in the assumptions are considered to be arbitrary and independent. Under these assumptions, all system states and transition probabilities between them are analyzed based on a semi-Markov theory and a regenerative point technique. Markov renewal equations are constructed with the convolution of the cumulative distribution function of system time in each state and corresponding transition probability. By using the Laplace transform to solve these equations, the mean time from the initial state to system failure is derived. The optimal preventive maintenance policy that will provide the optimal preventive maintenance cycle is identified by maximizing the mean time from the initial state to system failure, and is determined in the form of a theorem. Finally, a numerical example and simulation experiments are shown which validated the effectiveness of the policy.     

A δ-shock maintenance model for a deteriorating system

In this paper, a δ-shock maintenance model for a deteriorating system is studied. Assume that shocks arrive according to a renewal process, the interarrival time of shocks has a Weibull distribution or gamma distribution. Whenever an interarrival time of shocks is less than a threshold, the system fails. Assume further the system is deteriorating so that the successive threshold values are geometrically nondecreasing, and the consecutive repair times after failure form an increasing geometric process. A replacement policy N is adopted by which the system will be replaced by an identical new one at the time following the Nth failure. Then the long-run average cost per unit time is evaluated. Afterwards, an optimal policy N^* for minimizing the long-run average cost per unit time could be determined numerically.     

具有修理延迟的两不同部件冷贮备系统的可靠性分析

研究了有修理延迟的两个不同部件和两个修理工组成的冷贮备系统.假定部件的工作寿命服从一般分布,故障后的延迟修理时间和修理时间均服从指数分布.利用马尔可夫更新过程、拉普拉斯变换和拉普拉斯-司梯阶变换工具,得到了系统的首次故障前时间、可用度和平均故障次数等可靠性指标.     

有两种故障状态的两部件串联系统的预防维修策略

本文研究的是由两个部件串联组成且有两种故障状态的系统的预防维修策略, 当系统的工作时间达到T时进行预防维修, 预防维修使部件恢复到上一次故障维修后的状态。每个部件发生故障都有两种状态, 可维修和不可维修。当部件的故障为可维修故障时, 修理工对其进行故障维修, 且每次故障维修后的工作时间形成随机递减的几何过程, 每次故障后的维修时间形成随机递增的几何过程。当部件发生N次可维修故障或一次不可维修故障时进行更换。以部件进行预防维修的间隔和更换前的可维修故障次数N组成的二维策略(T, N) 为策略, 利用更新过程和几何过程理论求出了系统经长期运行单位时间内期望费用的表达式, 并给出了具体例子和数值分析。     

Extended optimal inspection policies for a system in storage

A system such as missiles and spare parts of aircraft has to perform a normal operation in a severe environment at any time when it is used. However, the system is in storage for a long time from the delivery to the usage and its reliability goes down with time. Thus, a system in storage should be inspected and maintained at periodic times to hold a higher reliability than is prespecified.The following inspection model is considered: A system has three types of units, where unit 1 is maintained, unit 21 is not maintained but is replaced and unit 22 is neither maintained nor replaced. The system is overhauled if its reliability becomes lower than a prespecified probability. The number of replacements and time until overhaul are derived. Using these results, the average cost is obtained and both an optimal inspection time and an optimal replacement time to minimize it are numerically discussed.     

The average optimality of a repair-limit replacement policy

We consider a minimal-repair and replacement problem of a reliability system whose state at a failure is described by a pair of two attributes, i.e., the total number of its past failures and the current failure level. It is assumed that the system is bothered by more frequent and more costly failures as time passes. Our problem is to find and/or characterize a minimal-repair and replacement policy of minimizing the long-run average expected maintenance cost per unit time over the infinite time horizon. Formulating the problem as a semi-Markov decision process, we show that a repairlimit replacement policy is average optimal. That is, for each total number of past system failures, there exists a threshold, called a repair limit, such that it is optimal to repair minimally if the current failure level is lower than the repair limit, and to replace otherwise. Furthermore, the repair limit is decreasing in the total number of past system failures.     

An optimal age maintenance for an M/G/1 queueing system

This paper discusses an optimal age maintenance scheme for a queueing system. Customers arrive at the system according to a Poisson process. They form a single queue and are served by a server with general service distribution. The system fails after a random time and corrective maintenance is performed at the failure. A preventive maintenance is also performed if the system is empty at age T where ‘age’ refers to the elapsed time since the previous maintenance was completed. If the system is not empty at age T, the system is used until it fails. At the failure, the customers in the system are lost and the arriving customers during the maintenance are also lost. By renewal theory, we study the optimal value of T which minimizes the average number of lost customers over an infinite time horizon.