有优先权且工作故障与贮备故障后的修理时间不相同的温贮备系统的可靠性分析

为了解决开关寿命为连续随机变量且部件工作故障的修理时间与贮备故障后的修理时间各不相同的问题,利用Markov过程理论和Laplace变换方法,研究了有优先权的两不同型部件和两不同修理工组成的温贮备可修系统.假定部件的工作寿命、贮备寿命、工作故障的修理时间和贮备故障的修理时间均服从不同的指数分布,得到了该系统的可靠度Laplace变换和系统的首次故障前平均时间的解析表达式.     

有优先权三不同部件温贮备可修系统可靠性分析

针对由三个不同部件,一个完全可靠的开关和一个修理设备组成的温贮备可修系统,建立了部件的工作寿命,贮备寿命,工作故障后的修理时间和贮备故障后的修理时间均服从不同参数的指数分布的数学模型,利用Markov型可修系统的研究方法,并采用MATLAB软件给出了该系统的首次故障前的平均时间、可用度和故障频率等可靠性指标的表达式.     

部件有两类故障状态且修理设备可更换的并联可修系统分析

本文考虑由两个同型部件组成的并联可修系统,每个部件有两类故障状态,部件故障后立即修理,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均服从指数分布,部件发生故障后的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,求得系统的有关可靠性指标和修理设备的闲期长度和"广义忙期"长度等一系列结果.     

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.     

具有单重休假和修复不如新的两部件并联系统

为了解决由"修复非新"部件组成的具有休假的可修型系统,运用几何过程理论、补充变量法和拉普拉斯变换工具,研究了由两个不同型部件和一个修理工组成的可修型并联系统.假设两个部件的工作寿命和修理时间均服从不同的指数分布,修理工可休假,对部件1的修理是几何修理而对部件2的修理则是修复如新,得到了系统的可用度、可靠度和系统首次故障前平均时间等可靠性指标.成果具有一定的理论和实际意义.     

有优先权两部件温贮备可修系统的模糊可靠性

利用普通可靠性和模糊可靠性的基础理论，在开关完全可靠的情况下，建立了有优先权两个不同型部件和一个修理设备组成的温贮备Markov可修系统的模糊可靠性数学模型，利用模糊数学的原理和方法、LS变换推导出该模型的一些模糊可靠性指标。     

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.     

两个同型部件温贮备系统的几何过程模型

利用可靠性理论,研究了两个同型部件和一个修理工组成的可修型温贮备系统.假设两个部件的工作寿命、贮备寿命、故障后的修理时间和贮备故障后的修理时间均服从不同的指数分布,在工作故障和贮备故障都不能"修复如新"的情况下,运用几何过程理论、拉普拉斯变换和补充变量方法得出该模型的一些可靠性指标.     

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.     

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.     

Mixture distributions for modelling demand during lead time

A mixture distribution approach to modelling demand during lead time in a continuous-review inventory model is described. Using this approach, both lead time and demand per unit time can follow state-dependent distributions. By using mixtures of truncated exponentials functions to approximate these distributions, mixture distributions that can be easily manipulated in closed form can be constructed as the marginal distributions for lead time and demand per unit time. These are then used to approximate the mixture of compound distributions for demand during lead time. The technique is illustrated by first applying it to a ‘normal-gamma’ inventory problem, then by modelling a problem with empirical distributions for lead time and demand per unit time.     

服务系统中位相型分布的随机比较

本文运用应用概率中的随机占优研究位相型(PH)分布的随机比较问题,具体给出在一阶、二阶随机占优下比较两个离散PH分布或两个连续PH分布的充分条件及充分必要条件。研究表明,比较两个离散PH分布可变性的条件与比较两个连续PH分布可变性的条件不同,在二阶随机占优意义下比较两个连续PH分布的条件与均值无关,而比较两个离散PH分布的条件与均值有关。本文的结果可用于研究PH分布的最小变异系数问题和可变性问题,也可用于研究带有PH到达间隔或PH服务的排队系统中到达过程或服务时间可变性对系统队长或等待时间的影响。     

The Numerical Generation of Lead Time Demand Distributions for Inventory Models

This paper presents a general method for computing a lead time demand distribution from the basic distributions of order quantity, orders per unit time, and lead time. These distributions are specified numerically and can therefore be derived directly from historical data.     

The Analysis of a General Input Queue with N Policy and Exponential Vacations

This paper studies a single removable server in a G/M/1 queueing system with finite capacity where the server applies an N policy and takes multiple vacations when the system is empty. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining interarrival time, to develop the steady-state probability distributions of the number of customers in the system. The method is illustrated analytically for exponential and deterministic interarrival time distributions. We establish the distributions of the number of customers in the queue at pre-arrival epochs and at arbitrary epochs, as well as the distributions of the waiting time and the busy period.     

On the Behaviour of Complex Systems with Regard to Dependability

Journal of the Operational Research Society - In Part I, a Complex System consisting of n components having a wide class of inter-failure time distributions and general repair time distributions...     

具有位相型修理的离散时间可修排队系统

本文研究了具有一般独立输入，位相型修理的离散时间可修排队系统，假定服务台对顾客的服务时间和服务台寿命服从几何分布，运用矩阵解析方法我们给出系统嵌入在到达时刻的稳态队长分布和等待时间分布，并证明这些分布均为离散位相型分布．我们也得到在广义服务时间内服务台发生故障次数的分布，证明它服从一个修正的几何分布．我们对离散时间可修排队与连续时间可修排队进行了比较，说明这两种排队系统在一些性能指标方面的区别之处．最后我们通过一些数值例子说明在这类系统中顾客的到达过程、服务时间和服务台的故障率之间的关系．     

Probability Distribution of Solution Time in GRASP: An Experimental Investigation

A GRASP (greedy randomized adaptive search procedure) is a multi-start metaheuristic for combinatorial optimization. We study the probability distributions of solution time to a sub-optimal target value in five GRASPs that have appeared in the literature and for which source code is available. The distributions are estimated by running 12,000 independent runs of the heuristic. Standard methodology for graphical analysis is used to compare the empirical and theoretical distributions and estimate the parameters of the distributions. We conclude that the solution time to a sub-optimal target value fits a two-parameter exponential distribution. Hence, it is possible to approximately achieve linear speed-up by implementing GRASP in parallel.     

随机环境中马氏链的首达分布矩(英文)

After defining generating functions,this paper discusses their properties,and then provides a sufFcient and necessary condition for a finite property of the moments of first entrance time distributions of Markov chains in random environments by generating functions.Finally,the paper obtains relevant conclusions of the moments of first entrance time distributions.     

On waiting time distributions associated with compound patterns in a sequence of multi-state trials

In this article, waiting time distributions of compound patterns are considered in terms of the generating function of the numbers of occurrences of the compound patterns. Formulae for the evaluation of the generating functions of waiting time are given, which are very effective computational tools. We provide several viewpoints on waiting time problems associated with compound patterns and develop a general workable framework for the study of the corresponding distributions. The general theory is employed for the investigation of some examples in order to illustrate how the distributions of waiting time can be derived through our theoretical results. This research was partially supported by the ISM Cooperative Research Program (2006-ISM·CRP-2007).     

Hierarchy of islands in conservative systems yields multimodal distributions of FTLEs

We investigate the motion in a chaotic layer of conservative systems using finite time Lyapunov exponents (FTLEs). For long finite time spans we find the distributions of FTLEs to be multimodal. Due to stickiness near islands of regular motion, the trajectory can spend a long time in their vicinity. The higher the order of an island in the hierarchy of islands, the smaller is the value of the largest FTLE. Using this connection, we explain the occurrence of multimodal distributions of FTLEs as a result of an overlap of individual distributions of FTLEs, each corresponding to the motion near islands of different orders.