可修复复杂系统脆性故障的研究

提出了可修复复杂系统的脆性概念,主要针对可修复复杂系统的脆性及其特性进行研究,建立了无储备和有储备可修复复杂系统的结构方程模型,用范数指标函数作为衡量控制变量的标准研究了可修复复杂系统的最优控制问题.     

故障时间任意分布的两部件可修复系统解的适定性分析

讨论了一个由两个部件并联组成的可修复冗余系统模型,修复后的故障系统恢复如新.在假设修复函数有界的条件下,给出了C_0-半群的生成元(系统算子)对应的柯西问题的解的适定性分析.     

两同型部件冷贮备可修系统主算子性质

研究了两同型部件冷贮备可修系统.运用C_0半群理论,通过修复率均值的观念,对系统主算子的谱上界进行了估值,并得到该谱上界即为系统部件修复率均值的相反数.然后运用了共尾的概念及相关的理论,得到了系统主算子的谱上界与系统主算子产生的半群的增长界相等,从而得到其增长界也是修复率均值的相反数.     

可修复系统任务可靠度的 fiducial 界限

一、前言对于不可修复的系统的可靠度的置信界限的讨论已有许多文章,无论是经典法,还是Bayes 法等都有若干结果.对于可修复系统的某些统计分析文章,70年以来也逐渐增多起来,逐渐为人们所关心.Ascher 自1968年以来陆续发表了许多文章,对可修复系统提出了“坏如旧”的新概念,并提出采用非平稳 Poisson 过程的模型来描述可修复系统的失效过程.同时还有许多人对非平稳 Poisson 过程以及 Weibull 过程等的统计分析工作也得到了许多结果.本文所讨论的问题是:对可修复系统可靠度和任务可靠度给出 fiducial 严格的界限和近似的界限.本文还讨论了如何利用可修复子系统的观察数据,得到串联系统可靠度和任务可靠度的 fiducial 界限.     

具有临界和非临界人为故障的人-机系统解的存在唯一性及半离散化

研究了具有临界和非临界人为故障率,且修复时间任意分布的可修复的人-机系统模型.利用初等方法将系统转换为8维Banach空间下的Volterra积分方程,得到系统非负解存在且唯一.并讨论了系统解的逼近.     

具有常规原因和人为错误的两个不同部件平行系统解的性质

讨论了一个由于常规原因和人为错误引起故障的两不同部件并行系统的模型,修复后的故障系统恢复正常.在假设修复率非常数的前提下,运用纯分析的方法给出了两不同部件并行系统解的性质,绕过了该系统解是否存在的问题.     

随机选择修理工的可修复系统指数稳定性分析

讨论了一个随机选择修理工的可修复系统解的指数稳定性,首先通过对积分微分方程组描述的可修复系统生成的系统算子的本质谱的增长性约束和扰动后本质谱半径的变化情况进行分析,进而得到了可修复系统解的指数稳定性.     

两同型部件温贮备可修系统主算子性质

研究了两同型部件温贮备可修系统.运用C_0半群理论,通过修复率均值的观念,对系统主算子的谱上界进行了估值,并得到该谱上界即为修复率均值的相反数.然后运用了共尾的概念及相关的理论,得到了系统主算子的谱上界与系统主算子产生的半群的增长界相等,从而得到其增长界也是修复率均值的相反数.     

刮板沉降箱式除尘可修复系统的适定性

研究了修复不如新情形下刮板沉降箱式除尘可修复系统的适定性问题.首先将系统方程转化为Banach空间下的抽象Cauchy问题,进一步通过线性算子半群理论证明了系统的适定性.     

一类修复不如新的可修复系统的可靠性分析

用增补变量的方法建立了在人为错误下修复不如新的两相同部件并联可修复系统.通过选取空间和定义系统算子,将模型方程转化成为了抽象Cauchy问题.然后利用线性算子半群理论研究了系统解的存在唯一性和渐近稳定性,进一步对系统的可用度做了比较分析.     

A reliability semi‐Markov model involving geometric processes

We consider a semi‐Markov process that models the repair and maintenance of a repairable system in steady state. The operating and repair times are independent random variables with general distributions. Failures can be caused by an external source or by an internal source. Some failures are repairable and others are not. After a repairable failure, the system is not as good as new and our model reflects that. At a non‐repairable failure, the system is replaced by a new one. We assume that external failures occur according to a Poisson process. Moreover, there is an upper limit N of repairs, it is replaced by a new system at the next failure, regardless of its type. Operational and repair times are affected by multiplicative rates, so they follow geometric processes. For this system, the stationary distribution and performance measures as well as the availability and the rate of occurrence of different types of failures in stationary state are calculated. Copyright © 2002 John Wiley & Sons, Ltd.     

Stationary availability of a semi‐Markov system with random maintenance

We consider a reparable system with a finite state space, evolving in time according to a semi‐Markov process. The system is stopped for it to be preventively maintained at random times for a random duration. Our aim is to find the preventive maintenance policy that optimizes the stationary availability, whenever it exists. The computation of the stationary availability is based on the fact that the above maintained system evolves according to a semi‐regenerative process. As for the optimization, we observe on numerical examples that it is possible to limit the study to the maintenance actions that begin at deterministic times. We demonstrate this result in a particular case and we study the deterministic maintenance policies in that case. In particular, we show that, if the initial system has an increasing failure rate, the maintenance actions improve the stationary availability if and only if they are not too long on the average, compared to the repairs ( a bound for the mean duration of the maintenance actions is provided). On the contrary, if the initial system has a decreasing failure rate, the maintenance policy lowers the stationary availability. A few other cases are studied. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

修理有延迟且修理设备可更换的多状态可修系统的可靠性分析

本文研究修理有延迟且修理设备可更换的单部件多状态可修系统.利用更新过程理论,得到了系统的可靠性指标.通过引入修理设备的"广义忙期",简洁地讨论了修理设备感兴趣的许多可靠性指标,得到一系列重要结果.     

修理设备可更换且有修理延迟的N部件串联系统分析

假定部件的寿命服从指数分布,修理延迟时间和修理时间均服从任意分布,并且修理设备的寿命服从指数分布,其更换时间服从任意分布的情况下,利用马尔可夫更新过程理论和拉普拉斯变换工具,研究了修理有延迟且修理设备可更换的n部件串联可修系统,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,提出了一种新的分析技术,讨论了修理设备的可靠性指标,得到修理设备的一些重要可靠性结果.     

修理设备可更换和修理延迟的两类故障状态并联可修系统

考虑两同型部件组成的并联可修系统,每个部件有两类故障状态,部件故障后修理有延迟,且修理设备在修理故障部件的过程中也可能发生故障.假定部件的寿命和修理设备的寿命服从指数分布,部件发生故障后的修理延迟时间、修理时间和修理设备故障后的更换时间均服从一般分布,利用马尔可夫更新过程理论和拉普拉斯变换工具,求得了系统有关的可靠性指标.     

Reliability analysis of a multistate system with a replaceable repair facility

This paper considers a one-unit multistate repairable system where the repair facility is subject to failure and can be replaced by a new one after it fails. By using renewal theory, we obtain some reliability quantities of the system and the repair facility.Project supported by the National Natural Science Foundation of China.     

Setting expediting repair policy in a multi-echelon repairable-item inventory system with limited repair capacity

Inventory systems with limited repair capacity are affected by congestion externalities, caused by use of a shared service. There is incompatibility between individual and system optimisation in considering congestion externalities. Three models are described that investigate the congestion effect in a multi-echelon inventory system which has two modes of repair, each with a limited repair capacity. An expanding repair policy employed by the bases in order to choose which repair mode to use is described and compared with different expediting policies related to congestion externalities. The expanding repair policy that considers congestion externalities was found to lead to better system performance measurement than an expanding policy with no congestion. The results of the numerical experiment indicate that the model that ignores congestion externalities—that is, the model that measures each base as an individual—leads to poorer performance measurement for every expediting repair policy, and particularly for the optimal expediting repair policy.     

泊松冲击下单部件混合贮备系统可靠性分析

研究的是泊松冲击下由三同型部件组成的单部件混合贮备系统可靠性.在系统三部件分别为工作部件、温贮备部件和冷贮备部件假定下,且假定三部件在工作过程中都是接着工作、修理、冷贮备、温贮备、工作依次进行状态转移,同时假设部件寿命和维修时间都服从指数分布,利用基本概率理论和马尔可夫过程理论分别对不可修和可修两类系统进行讨论得到相关可靠性指标.     

一类具有可修复储备部件的人-机系统解的半离散化

针对一个具有两个运行部件和一个储备部件,考虑系统通常故障的发生,且系统故障修复时间服从一般分布的人-机系统模型,对系统模型中修复率用初等阶梯函数进行逼近,给出了系统的半离散化模型,为进一步数值计算打下理论基础.