N部件串联可修系统的一个新模型及其可靠性分析

本文研究N部件串联可修系统的一个新模型,该模型在经典n部件串联可修系统中引入了修理工可单重延误休假的概念,并且考虑了修理设备可能发生故障而对整个系统可靠性造成的影响。假定修理工的延误休假时间、部件的寿命和修理设备的寿命均服从指数分布,部件的修理时间、修理设备的更换时间和修理工的休假时间均服从一般连续型分布,通过使用补充变量法和广义马尔可夫过程方法得到了系统和修理设备的一些重要可靠性指标。     

修理工可单重休假的带有一个冷贮备部件的Gaver并联系统

本文研究了修理工可单重休假的带有一个冷贮备部件的Gaver并联可修系统。假定部件的工作时间服从指数分布,修理时间和修理工的休假时间均服从一般连续分布。利用向量Markov过程理论和Laplace变换的方法,求出了系统可靠度的Laplace变换,系统首次故障前平均时间的表达式,系统的稳态可用度和稳态故障频度等可靠性指标。此外,还建立了系统效益模型并通过数值比较分析了各参数对系统效益的影响。     

修理工可单重休假带有一个冷贮备部件并联系统的适定性

本文运用线性算子半群理论研究修理工可单重休假的带有一个冷贮备部件的Gaver并联可修系统的适定性问题．文中假定部件的工作时间服从指数分布,修理时间和修理工的休假时间均服从一般连续分布．通过对描述该系统行为的偏微分方程组的规范化,并引入系统的状态空间,主算子及其定义域,我们将该系统方程转化成Banach空间中的抽象的Cauchy问题．然后,运用泛函分析中的Hille-Yosida定理、Phillips定理与Fattorini定理,我们证明了该系统存在唯一的、满足概率性质的正时间依赖解．     

修理工N-策略休假的带有温贮备的可修系统的可靠性分析

修理工休假的多部件温贮备可修系统模型广泛应用于电力系统,医疗设备系统和制造系统等领域.本文研究了修理工N-策略休假的多部件温贮备可修系统,探讨该系统的稳态可用度和稳态故障频度.利用Markov过程理论和递归迭代的方法,求出了系统稳态概率的迭代计算公式,并进一步得到了系统稳态可用度和稳态故障频度.     

服务员休假的生产服务库存模型的稳态分析及最优生产策略

将服务员休假与生产服务库存相结合，研究带有服务员休假的 M/M/1 生产服务库存系统模型。需求 (顾客) 的到达过程服从 Poisson 过程，顾客的服务时间和每个产品的生产时间都服从指数分布。当系统库存为零时，服务员开始随机长度的休假。假设休假时间服从指数分布。首先，利用拟生灭过程理论给出了系统的稳态平衡条件。其次，对忽略服务时间的生产服务库存系统模型进行了稳态分析，得到了此系统的稳态概率的明显的解析表达式，进而证明了系统的稳态概率分布具有乘积解形式的结构。在此基础上，进一步得到了系统的一些稳态性能指标和费用函数的计算公式，数值求解了模型的最优 $(s,S)$ 库存策略，并研究系统的一些参数对性能指标、最优策略和最优费用的影响。     

兼职辅助业务的多修理工机器维修模型

本文研究了多修理工同时兼职辅助业务的机器维修模型,这个模型可以归结为多服务台同步休假的有限源排队问题。利用拟生灭过程的方法,给出了稳态下机器故障数的分布和等待维修时间的分布。在特殊情况下模型退化成单修理工兼职辅助业务的机器维修模型和经典无休假的机器维修模型,得到了和前人研究成果一致的稳态分布。数值例子说明本文在系统优化方面的应用。     

启动-关闭型多级适应性休假Mx/G/1可修排队的可靠性分析

考虑带启动时间和关闭时间(延迟休假)的多级适应性休假Mx／G(M／G)／1可修排队系统,在假定启动时间、关闭时间、服务台的修理时间和休假时间都服从一般分布的情况下,通过引入服务台的“广义忙期”,采用一种较简单分析方法讨论了有关服务台的许多感兴趣的可靠性指标,得到了一些重要的可靠性结果。     

启动一关闭型多级适应性休假M^x／G／1可修排队的可靠性分析

考虑带启动时间和关闭时间（延迟休假）的多级适应性休假M^x／G（M/G）／1可修排队系统,在假定启动时间、关闭时间、服务台的修理时间和休假时间都服从一般分布的情况下,通过引入服务台的“广义忙期”,采用一种较简单分析方法讨论了有关服务台的许多感兴趣的可靠性指标,得到了一些重要的可靠性结果。．     

修理设备可更换且修理延迟的两同型部件并联可修系统

本文假定部件的寿命服从指数分布,其修理延迟时间和修理时间均服从一般分布,并且修理设备的寿命服从指数分布,其更换时间服从一般分布,利用马尔可夫更换过程理论,研究了修理设备可更换且修理有延迟的两同型部件的并联可修系统,求得了系统的可用度和(0,t)时间内的平均故障次数。进一步,在定义修理设备“广义忙期”下,利用全概率分解,提出了分析修理设备可靠性指标的一种新技术,并得到修理设备的一系列重要可靠性结果。     

基于PH分布的两部件并联系统可靠性模型分析

在系统可靠性建模过程中,通常假设部件寿命和维修时间等服从指数分布等典型分布,这样做会导致模型的约束条件过于严格,缩小了所研究模型的适用范围.采用Phase-type(PH)分布来构建模型,研究了包含2个不同部件的并联系统,考虑系统具有单一维修台,假设部件寿命和维修时间分别服从不同的PH分布,构建了描述能力更强的系统可靠性模型,得出了明确的系统稳态可用度、首次故障前平均工作时间、稳态故障频度等一系列相关可靠性参数的解析式.最后,通过算例分析证明了该方法的正确性和适用性.     

An optimal replacement policy for a repairable system based on its repairman having vacations

This paper studies a cold standby repairable system with two different components and one repairman who can take multiple vacations. If there is a component which fails and the repairman is on vacation, the failed component will wait for repair until the repairman is available. In the system, assume that component 1 has priority in use. After repair, component 1 follows a geometric process repair, while component 2 can be repaired as good as new after failures. Under these assumptions, a replacement policy N based on the failed times of component 1 is studied. The system will be replaced if the failure times of component 1 reach N. The explicit expression of the expected cost rate is given, so that the optimal replacement time N^? is determined. Finally, a numerical example is given to illustrate the theoretical results of the model.     

Performance analysis and optimization of a machine repair problem with warm spares and two heterogeneous repairmen

In this paper, we study a machine repair problem with warm spares and two heterogeneous repairmen from the view points of both queueing and reliability. In this system, the first repairman is always available for serving the failed units, while the second repairman leaves for a vacation of random length when the number of failed units is less than N. We obtain expressions for the steady-state probabilities of the system by solving the steady-state probability equations iteratively. Then, we obtain some performance measures for the system. We also obtain some performance measures of reliability for the system such as the steady-state availability, the steady-state failure frequency and the mean time between the system failures. Moreover, we present derivations of the mean time taken until the first failure of the system. A cost model is developed to determine the optimum value N while the system availability is maintained at a certain level. A sensitivity analysis is also performed.     

Performance and cost analysis of a Geom/G/1 (G, SV) system

In this paper, a gate service Geom/G/1 queue system with single vacation is analyzed. Firstly, a gate service policy and single vacation are introduced in detail, the expected number of customers in the system at the beginning instant of a service period is obtained. Next, the Probability Generating Function (P.G.F.) of the stationary queue length is obtained by using regeneration cycle approach. Then the P.G.F. of the waiting time is derived under the condition of the independence between the arrival process and the waiting time. Moreover, the P.G.Fs. of the service period, the vacation period and the idle period are obtained, and the mean length of three periods are also obtained. Cost model is formulated to determine the optimal expected vacation length. Finally, based on numerical results, the relations of the performance measures and traffic intensity are discussed.     

阈值调控的GI/Geo/1多重工作休假排队

在随机服务系统中,减少系统能源消耗,提高服务效率,是人们关注的焦点．基于此目的,本文加入阈值和休假中止策略,具体分析了离散时间GI/Geo/1工作休假排队系统．首先,建立了顾客到达前夕二维嵌入马尔可夫链,给出了GI/M/1型结构矩阵．其次,应用矩阵分析方法得到系统稳态队长分布,并进一步求得系统稳态下的平均队长和平均逗留时间等指标．最后,通过Matlab仿真软件,对模型中的性能指标给予刻画和展示,结果表明平均队长和平均逗留时间随阈值的增大而增大,随休假服务率的增加而减少．本文的结果将为交换虚通道以及无线网络等方面的研究提供一定的参考．     

Reliability analysis for a circular consecutive-2-out-of-n:F repairable system with priority in repair

A circular consecutive-2-out-of-n:F repairable system with one repairman is studied in this paper. When there are more than one failed component, priorities are assigned to the failed components. Both the working time and the repair time of each component is assumed to be exponentially distributed. Every component after repair is as good as new. By using the definition of generalized transition probability and the concept of critical component, we derive the state transition probability matrix of the system. Methodologies are then presented for the derivation of system reliability indexes such as availability, rate of occurrence of failure, mean time between failures, reliability, and mean time to first failure.     

A Mean Value Analysis of the Travelling Repairman Problem

We consider the machine repairman problem where the machines are spatially distributed and repaired by a travelling serviceman. We assume identical machines with exponential up times and general repair times. We also assume that the travel times between pairs of locations have identical, but arbitrary distributions. Assuming a work-conserving, non-preemptive service discipline, a semi-Markov model is developed and various performance measures are evaluated. Some applications of the model are discussed. The model developed here, is used elsewhere to develop approximations for a more realistic situation where machines are non-identical and travel time distributions between pairs of locations are also non-identical.     

Performability indicators for the traffic analysis of wide area networks

In this paper, a repairable circular consecutive-k-out-of-n:F system with one repairman is studied. It is assumed that the working time and the repair time of each component are both exponentially distributed and every component after repair is ‘as good as new’. Each component is classified as either a key component or an ordinary component. Key components have priority in repair when failed. By using the definition of generalized transition probability, the state transition probabilities of the system are derived. Important reliability indices are evaluated for an example.