Interval reliability for aggregated Markov repairable system with repair time omission

In this paper, Markov models of repairable systems with repair time omission are considered whose finite state space is grouped into two sets, the set of working states, W, and the set of failed states, F. If the system enters failed states from a working state at any instance, and sojourns at the failed states F less than a given nonnegative critical value τ, then the repair interval can be omitted from downtime records. Otherwise, If the system enters failed states from a working state at any instance, and sojourns at the failed states F more than the given nonnegative critical value τ, then the repair interval cannot be omitted from downtime records. In terms of the assumption, a new model is developed. The focus of attention is the new model’s availability, interval reliability and interval unreliability. Several results are derived for these reliability indexes for the new model. Some special cases and numerical examples are given to illustrate the results obtained by using Maple software in the paper.     

泊松冲击下冷贮备可修系统的可靠性分析

本文研究了一类由有限个同质部件和一个修理工组成的冷贮备可修系统在随机冲击下的可靠性问题。假设冲击以泊松过程到达。当冲击到达时,它会独立地对系统中工作的部件产生影响,而不会对冷贮备部件产生影响。每次冲击的量都服从某一确定的分布,受冲击的部件以一定的概率发生故障,其故障概率是冲击量的函数,当工作的部件发生故障时,下一个冷贮备部件立即开始工作,当所有部件故障时,系统故障,故障部件按故障顺序进行修理,修理时间服从指数分布,故障部件能被修理如新。本文显式给出了系统首次故障前平均时间、稳态可用度、稳态故障频度等可靠性指标。     

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.     

Reliability analysis of a stand-by system with repair and intermediate stocks for failed and repaired units

In this paper we give a reliability analysis of a stand-by system with repair, consisting of N working and N^R stand-by units. Failed and repaired units are collected in intermediate stocks. Concerning the delivery from the intermediate stocks we consider two rules: (i) the collected units are delivered in fixed time intervals; (ii) the units will be delivered when there are k units accumulated. The system fails if a unit that has failed cannot be replaced by a stand-by unit. Using a point process approach we derive approximations for the stationary availability and mean time between failures of the system. Numerical results show that the proposed approximations, which can be handled easily, work well.     

On the interaction between maintenance,spare part inventories and repair capacity for a k-out-of-N system with wear-out

In this paper we consider a k-out-of-N system with identical, repairable components under a condition-based maintenance policy. Maintenance consists of replacing all failed and/or aged components. Next, the replaced components have to be repaired. The system availability can be controlled by the maintenance policy, the spare part inventory level, the repair capacity and repair job priority setting. We present two approximate methods to analyse the relation between these control variables and the system availability. Comparison with simulation results shows that we can generate accurate approximations using one of these models, depending on the system size.     

System availability in a shock model under preventive repair and phase‐type distributions

A device that can fail by shocks or ageing under policy N of maintenance is presented. The interarrival times between shocks follow phase‐type distributions depending on the number of cumulated shocks. The successive shocks deteriorate the system, and some of them can be fatal. After a prefixed number k of nonfatal shocks, the device is preventively repaired. After a fatal shock the device is correctively repaired. Repairs are as good as new, and follow phase‐type distributions. The system is governed by a Markov process whose infinitesimal generator, stationary probability vector, and availability are calculated, obtaining well‐structured expressions due to the use of phase‐type distributions. The availability is optimized in terms of the number k of preventive repairs. Copyright © 2009 John Wiley & Sons, Ltd.     

修复率可变化的表决系统可靠性分析

研究了具有维修速率可变化的k/n(G)表决可修系统,其中部件的工作时间和修理时间均服从负指数分布.开始时,当系统中的故障部件数小于某一阈值L时,修理工以较低的维修率修理故障的部件.如果修理工修理工作进展不顺利,故障部件数增加到阈值L时,将立即以较快的速度修理故障部件,此状态一直持续到系统中没有故障部件为止.使用马尔可夫过程理论和分析方法,得到了系统可用度、故障频度、系统首次故障前的平均时间等指标的表达式.进一步,讨论了不同条件下系统相关指标随系统参数变化的情况,并通过对特殊情形的讨论数值验证了所得结果的正确性.     

Selective maintenance for support equipment involving multiple maintenance actions

Selective maintenance is the process of identifying a subset among sets of desirable maintenance actions. Previous works use mathematical programming models for making selective maintenance decisions for production equipment and military vehicles, which perform sequences of missions and are repaired only between missions. In this paper, extensions of these models are proposed. First, system component life is assumed to follow Weibull distributions. Second, the decision-maker is given multiple maintenance options: minimal repair on failed components, replacement of failed components, and replacement of functioning components (preventive maintenance).     

Repair systems with exchangeable items and the longest queue mechanism

We consider a repair facility consisting of one repairman and two arrival streams of failed items, from bases 1 and 2. The arrival processes are independent Poisson processes, and the repair times are independent and identically exponentially distributed. The item types are exchangeable, and a failed item from base 1 could just as well be returned to base 2, and vice versa. The rule according to which backorders are satisfied by repaired items is the longest queue rule: At the completion of a service (repair), the repaired item is delivered to the base that has the largest number of failed items. We point out a direct relation between our model and the classical longer queue model. We obtain simple expressions for several probabilities of interest, and show how all two-dimensional queue length probabilities may be obtained. Finally, we derive the sojourn time distributions.     

Exact and approximation methods for dependability assessment of tram systems with time window

The transportation system examined in this paper is the city tram one, where failed trams are replaced by reliable spare ones. If failed tram is repaired and delivered, then it comes back on work. There is the time window that failed tram has to be either replaced (exchanged) by spare or by repaired and delivered within. Time window is therefore paramount to user perception of transport system unreliability. Time between two subsequent failures, exchange time, and repair together with delivery time, respectively, are described by random variables A, E, and D. A/E/D is selected as the notation for these random variables. There is a finite number of spare trams. Delivery time does not depend on the number of repair facilities. Hence, repair and delivery process can be treated as one with infinite number of facilities. Undesirable event called hazard is the event: neither the replacement nor the delivery has been completed in the time window. The goal of the paper is to find the following relationships: hazard probability of the tram system and mean hazard time as functions of number of spare trams. For systems with exponential time between failures, Weibull exchange and exponential delivery (so M/W/M in the proposed notation) two accurate solutions have been found. For systems with Weibull time between failures with shape in the range from 0.9 to 1.1, Weibull exchange and exponential delivery (i.e. W/W/M) a method yielding small errors has been provided. For the most general and difficult case in which all the random variables conform to Weibull distribution (W/W/W) a method returning moderate errors has been given.     

Reliability-based measures for a retrial system with mixed standby components

In this paper, we consider a retrial and repairable multi-component system with mixed warm and cold standby components. It is assumed that the failure times of primary (operating) and warm standby components follow exponential distributions. When a component fails, it is sent to a service station with a single server (repairman) and no waiting space. The failed component is repaired if the server is idle and it has to enter an orbit if the server is busy. The failed component in the orbit will try to get the repair service again after an exponentially distributed random time period. The repair time also has an exponential distribution. The mean time-to-failure, MTTF, and the steady-state availability, A_T(∞), are derived in this retrial and repairable system. Using a numerical example, we compare the systems with and without retrials in terms of the cost/benefit ratios. Sensitivity analysis for the mean time-to-failure and the steady-state availability are investigated as well.     

单调关联系统的条件失效元件数量

Coherent systems are very important in reliability,survival analysis and other life sciences.In this paper,we consider the number of failed components in an(n-k+1)-out-of-n system,given that at least m(m相似文献   

A standby system with two types of repair persons

A continuously monitored one‐unit system, backed by an identical standby unit, is perfectly repaired by an in‐house repair person, if achievable within a random or deterministic patience time (DPT), or else by a visiting expert, who repairs one or all failed units before leaving. We study four models in terms of the limiting availability and limiting profit per unit time, using semi‐Markov processes, when all distributions are exponential. We show that a DPT is preferable to a random patience time, and we characterize conditions under which the expert should repair multiple failed units (rather than only one failed unit) during each visit. We also extend the method when life‐ and repair times are non‐exponential. Copyright © 2009 John Wiley & Sons, Ltd.     

Cost-benefit analysis of one-server n-unit adaptive system with slow switch

This paper considers a shared parallel system consisting of n-units supported by single service facility to carry out both installation and repair of a unit. Initially, all the n units share the total load equally and when one or more units fail, they go for repair while the other surviving units share the entire load equally till the failed units are ready for operation after installation. The installation time (switchover time) of a repaired unit is assumed to be non-negligible and random. The system will be down when all the units are non-operative , Assuming that the failure rates are different when the units function under varying loads, the system characteristics, namely, (1) the expected up-time of the system during (0, t], (2) the expected repair time of the units which failed due to varying failure rates during (0, t] and (3) the expected time spent by the units in the installation state during the period (0, t], are obtained by identifying the system at suitable regeneration epochs. The repair time and the switchover time of the units are arbitrarily distributed. The failure rate of unit is assumed to be constant. It depends on the number of surviving units at any instant. The cost-benefit analysis is also carried out using these system characteristics     

Analysis of R out of N systems with several repairmen,exponential life times and phase type repair times: An algorithmic approach

An R out of N repairable system consisting of N independent components is operating if at least R components are functioning. The system fails whenever the number of good components decreases from R to R − 1. A failed component is sent to a repair facility having several repairmen. Life times of working components are i.i.d random variables having an exponential distribution. Repair times are i.i.d random variables having a phase type distribution. Both cold and warm stand-by systems are considered. We present an algorithm deriving recursively in the number of repairmen the generator of the Markov process that governs the process. Then we derive formulas for the point availability, the limiting availability, the distribution of the down time and the up time. Numerical examples are given for various repair time distributions. The numerical examples show that the availability is not very sensitive to the repair time distribution while the mean up time and the mean down time might be very sensitive to the repair time distributions.     

Evaluation of time-varying availability in multi-echelon spare parts systems with passivation

The popular models for repairable item inventory, both in the literature as well as practical applications, assume that the demands for items are independent of the number of working systems. However this assumption can introduce a serious underestimation of availability when the number of working systems is small, the failure rate is high or the repair time is long. In this paper, we study a multi-echelon repairable item inventory system under the phenomenon of passivation, i.e. serviceable items are passivated (“switched off”) upon system failure. This work is motivated by corrective maintenance of high-cost technical equipment in the miltary. We propose an efficient approximation model to compute time-varying availability. Experiments show that our analytical model agrees well with Monte Carlo simulation.     

Optimale Ersatzstrategie für ein System aus reparierbaren Elementen bei vorgegebener Verfügbarkeit

Zusammenfassung Ein System besteht aus einer festen Anzahl gleichzeitig eingesetzter Geräte. Es ist nur funktionsfähig, wenn alle Geräte funktionieren. Um dies sicherzustellen, ist ein Ersatzlager eingerichtet, das einen Vorrat neuer oder neuwertig reparierter Geräte enthält sowie eine gewisse Anzahl von Reparaturstellen, in denen die defekten Geräte repariert werden.Das zu lösende Problem besteht darin, durch einen Kostenvergleich die Anzahl der Reservegeräte und der Reparaturstellen so festzulegen, daß die Summe aller Kosten möglichst klein und eine vorgegebene Verfügbarkeit mindestens erreicht wird.Das Problem wurde analytisch gelöst und ein Rechenprogramm dazu geschrieben. Numerische Ergebnisse werden vorgelegt.

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Summary A system consists of a determined number of equipments which are used simultaneously. It is only operational, if all equipments are working properly. A replacement store comprising a stock of new or as new repaired equipments as well as a certain number of repair stations where the damaged equipments are being repaired, are being established for this purpose.The problem to be solved is to determine the number of spare equipments and of repair stations by means of a comparison of costs such as to keep the total amount of costs as low as possible and to obtain at least the given availability.The problem has been solved analytically and a respective computer programme has been prepared. Numerical results are being submitted.

     

Preventive maintenance for homogeneous and heterogeneous systems

We consider optimal preventive maintenance for homogeneous and heterogeneous systems with major (critical) and minor (noncritical) failures. A major failure results in a replacement of a failed system, whereas minor failures can be minimally instantaneously repaired. Distinct from the homogeneous case, where the process of minimal repairs is the Poisson process, the process of minimal repairs in the heterogeneous case is the mixed Poisson process that does not possess the memoryless property. This enables considering the number of minimal repairs as the decision parameter for the corresponding optimal preventive maintenance policy. The proposed approach is theoretically justified, and the detailed illustrative numerical examples are presented.     

Poisson冲击下的$k/n(G)$系统的可靠性分析

本文研究了一类Poisson冲击下的$k/n(G)$系统(即$k$-out-of-$n$: $G$系统). 假定冲击的到达数形成一个参数为$\lambda$的Poisson过程, 且冲击的量服从某一分布. 当每次冲击到达时, 对系统中工作的部件独立地产生影响. 进而假定每一部件以一定的概率故障, 概率值是冲击量的函数. 且各次冲击独立地对系统造成损失, 直到工作部件数少于$k$系统故障为止. 在这些假定下, 我们获得了系统的可靠度函数和系统的平均工作时间. 进一步, 假定系统是可修的, 系统中有一个维修工, 并根据``先坏先修’’的维修规则对故障部件进行维修. 在维修时间服从指数分布的假设下, 系统状态转移服从Markov过程. 对该系统我们建立了状态转移方程, 并求得了系统可用度、稳态下的平均工作时间、平均停工时间和系统失效频率等可靠性指标. 最后, 我们还给出了一个简单例子来演示讨论的模型.     

选择性维护决策的研究进展与挑战

在工业生产和军事领域中,生产设备或技术装备往往要求连续执行多个任务,并且在任务间隔期内需要对系统中老化或失效的部件进行维护以确保完成后续任务.然而,由于受有限的成本、时间、设备及人员等维护资源的限制,在任务间隔期内难以修复系统中的所有组成部件,决策者只能有策略地选择部分部件进行维护,从而最大程度地确保完成后续任务,这类维护决策问题被称为选择性维护.现主要介绍选择性维护决策的基本模型和特点,并从系统建模、维护程度、资源约束与资源消耗、任务特性与应用环境、优化算法五个方面综述国内外关于选择性维护决策的研究进展和发展动态,并讨论其发展趋势和挑战.