一般δ-冲击模型及其最优更换策略

本文讨论了一种具有一般δ-冲击的可修系统，我们不仅给出了该系统的一些可靠性指标，如系统的可靠度，系统平均工作时间，系统工作时间的极限分布等，而且对该可修系统的分布性质也进行了研究．在Poisson冲击下，我们证明了该系统的寿命分布是NBU的．在该系统为”修复非新”时，我们利用几何过程考虑了以系统的故障次数N为更换策略，以长期运行单位时间内的期望费用为目标函数，通过目标函数最小化确定了最优更换策略．最后我们给出了一个数值例子．     

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.     

基于两种不同延迟过程的退化系统之最优更换策略

将延迟几何过程进行推广并引入延迟α-幂过程,以用于处理退化过程会发生延迟且延迟发生的概率会随故障次数的增多而减小的系统.以系统的故障次数为更换策略,以平均费用率为目标函数,建立了维修更换模型,证明了最优维修更换策略的存在性.最后,通过一个数值例子验证了方法的有效性.     

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.     

基于休假时间的贮备系统的二维更换策略模型

研究两个不同型部件和一个修理工组成的冷贮备可修系统,在考虑了预防修和使用的优先权的条件下,以部件1的故障次数N及预防维修时长T为策略,利用几何过程和更新过程理论,建立了以修理工休假时间为目标函数,以费用率和停机时间为约束条件的优化模型.在部件1寿命分布函数已知的情况下,证明了系统经长期运行修理工平均休假时间随T是单调增加的,最后通过数值例子验证了最优的策略(T~*,N~*)的存在性.     

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.     

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.     

工作时间受限的单部件可修系统的维修策略

基于几何过程理论,研究了一类工作时间受限的单部件可修系统的最优更换策略问题.假定系统的维修时间和工作时间都服从一般分布,当工作时间低于预先给定的阈值φ,或当系统的维修次数达到N时,不再维修,而是更换上全新系统.利用更新过程理论,得到了系统平均故障频度和平均可用度等可靠性指标,并给出了系统长期运行单位时间期望效益函数的表达式,最后通过数值模拟讨论了下限阈值和工作次数对最优策略的影响.     

基于休假时间和基准可靠度的冷贮备二维预防维修策略

研究由两个不同型部件和一个修理工组成的冷贮备可修系统,其中部件1具有优先使用权.为了延长系统的工作时间,考虑对部件1进行非定期预防维修和故障维修相结合的维修策略,并以部件1的故障次数N和预防维修间隔T为二元维修策略(N,T),利用几何过程和更新过程等数学理论,建立以修理工单位时间内平均休假时间为目标函数、以费用率和平均停机时间为约束条件的优化模型,最后运用实例验证了模型的有效性.     

具有易损坏储备部件复杂可修系统解的半离散化

讨论了易损坏部件对系统的影响,且故障系统的修复时间是任意分布的.并对修复率μi(x)用初等阶梯函数进行逼近,给出了系统的半离散化模型,为进一步的数值计算打下基础.     

一个可修系统的最优更换模型

本文考虑了单部件、一个修理工组成的可修系统，在故障系统不能“修复如新”的前提下，我们利用几何过程，以系统年龄Ｔ为策略，选择最优的Ｔ使得系统经长期运行单位时间的期望效益达到最大．本文还在一定的条件下证明了最优更换策略Ｔ的唯一存在，且求出了系统经长期运行单位时间的最大期望效益的明显表达式．     

A deteriorating cold standby repairable system with priority in use

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. In this system, it is assumed that the working time distributions and the repair time distributions of the two components are both exponential and component 1 is given priority in use. After repair, component 2 is “as good as new” while component 1 follows a geometric process repair. Under these assumptions, using the geometric process and a supplementary variable technique, some important reliability indices such as the system availability, reliability, mean time to first failure (MTTFF), rate of occurrence of failure (ROCOF) and the idle probability of the repairman are derived. A numerical example for the system reliability R(t) is given. And it is considered that a repair-replacement policy based on the working age T of component 1 under which the system is replaced when the working age of component 1 reaches T. Our problem is to determine an optimal policy T^∗ such that the long-run average cost per unit time of the system is minimized. The explicit expression for the long-run average cost per unit time of the system is evaluated, and the corresponding optimal replacement policy T^∗ can be found analytically or numerically. Another numerical example for replacement model is also given.     

Renewal analysis of a replacement process

We consider a unit with a random lifetime which is replaced at renewal times by a new identical one regardless of whether it has failed before or not. For this random periodic replacement policy, we derive exact formulas for the cycle length, defined as the time between the replacements of two successive failed units, the stationary probability of the current unit to have failed, and the stationary and the transient distributions of the residual lifetime of the current unit.     

Optimal warranty policies for systems with imperfect repair

We investigate a system whose basic warranty coverage is minimal repair up to a specified warranty length. An additional service is offered whereby first failure is restored up to the consumers’ chosen level of repair. The problem is studied under two system replacement strategies: periodic maintenance before and after warranty. It turns out that our model generalizes the model of Rinsaka and Sandoh [K. Rinsaka, H. Sandoh, A stochastic model with an additional warranty contract, Computers and Mathematics with Applications 51 (2006) 179–188] and the model of Yeh et al. [R.H. Yeh, M.Y. Chen, C.Y. Lin, Optimal periodic replacement policy for repairable products under free-repair warranty, European Journal of Operational Research 176 (2007) 1678–1686]. We derive the optimal maintenance period and optimal level of repair based on the structures of the cost function and failure rate function. We show that under certain assumptions, the optimal repair level for additional service is an increasing function of the replacement time. We provide numerical studies to verify some of our results.     

An optimal replacement policy for a multistate degenerative simple system

In this paper, a degenerative simple system (i.e. a degenerative one-component system with one repairman) with k + 1 states, including k failure states and one working state, is studied. Assume that the system after repair is not “as good as new”, and the degeneration of the system is stochastic. Under these assumptions, we consider a new replacement policy T based on the system age. Our problem is to determine an optimal replacement policy T^∗ such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit expression of the average cost rate is derived, the corresponding optimal replacement policy can be determined, the explicit expression of the minimum of the average cost rate can be found and under some mild conditions the existence and uniqueness of the optimal policy T^∗ can be proved, too. Further, we can show that the repair model for the multistate system in this paper forms a general monotone process repair model which includes the geometric process repair model as a special case. We can also show that the repair model in the paper is equivalent to a geometric process repair model for a two-state degenerative simple system in the sense that they have the same average cost rate and the same optimal policy. Finally, a numerical example is given to illustrate the theoretical results of this model.     

有优先维修权和优先使用权的冷储备系统的几何过程模型

本文研究了一个由两个部件和一个维修工组成的可修型冷储备系统.假设两个部件的工作时间和维修时间都服从指数分布,对部件2的维修是修旧如新而对部件1则是几何维修,且对部件1给予优先使用和优先维修的权利,在这些假定下,我们运用几何过程理论和补充变量方法,得到了一些重要的可靠性指标如系统可靠度、可用度、系统首次故障前平均工作时间和系统瞬时故障率等.最后还给出了维修工空闲的概率.     

Optimal replacement policy based on maximum repair time for a random shock and wear model

We study a \(\delta \) shock and wear model in which the system can fail due to the frequency of the shocks caused by external conditions, or aging and accumulated wear caused by intrinsic factors. The external shocks occur according to a Bernoulli process, i.e., the inter-arrival times between two consecutive shocks follow a geometric distribution. Once the system fails, it can be repaired immediately. If the system is not repairable in a pre-specific time D, it can be replaced by a new one to avoid the unnecessary expanses on repair. On the other hand, the system can also be replaced whenever its number of repairs exceeds N. Given that infinite operating and repair times are not commonly encountered in practical situations, both of these two random variables are supposed to obey general discrete distribution with finite support. Replacing the finite support renewal distributions with appropriate phase-type (PH) distributions and using the closure property associated with PH distribution, we formulate the maximum repair time replacement policy and obtain analytically the long-run average cost rate. Meanwhile, the optimal replacement policy is also numerically determined by implementing a two-dimensional-search process.     

Hierarchical decision making in production and repair/replacement planning with imperfect repairs under uncertainties

In this paper, we analyse an optimal production, repair and replacement problem for a manufacturing system subject to random machine breakdowns. The system produces parts, and upon machine breakdown, either an imperfect repair is undertaken or the machine is replaced with a new identical one. The decision variables of the system are the production rate and the repair/replacement policy. The objective of the control problem is to find decision variables that minimize total incurred costs over an infinite planning horizon. Firstly, a hierarchical decision making approach, based on a semi-Markov decision model (SMDM), is used to determine the optimal repair and replacement policy. Secondly, the production rate is determined, given the obtained repair and replacement policy. Optimality conditions are given and numerical methods are used to solve them and to determine the control policy. We show that the number of parts to hold in inventory in order to hedge against breakdowns must be readjusted to a higher level as the number of breakdowns increases or as the machine ages. We go from the traditional policy with only one high threshold level to a policy with several threshold levels, which depend on the number of breakdowns. Numerical examples and sensitivity analyses are presented to illustrate the usefulness of the proposed approach.