Highly Efficient Monte-Carlo for Estimating the Unavailability of Markov Dynamic System
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摘要: 当马尔可夫系统规模较大时,需要采用蒙特卡罗方法计算其瞬态不可用度,如果系统的 不可用度很小,则需要采用高效率的蒙特卡罗方法.本文在马尔可夫系统寿命过程的积分方程的 基础上,给出了系统瞬态不可用度计算的蒙特卡罗方法的统一描述,由此设计了马尔可夫系统瞬 态不可用度计算的直接统计估计方法和加权统计估计方法.用直接仿真方法、拟仿真方法、基于 直接仿真的统计估计方法、基于拟方仿真的统计估计方法和加权统计估计方法计算了-可修 Con/3/30:F系统的瞬态不可用度.结果表明,由于同时采用了偏倚的抽样空间和逐次事件估计 量,加权统计估计方法的方差最小,当系统不可用度很小时,该方法效率最高.Abstract: Monte Carlo simulation has become an important tool for estimating the reliability and availability of dynamic system, since conventional numerical methods are no longer efficient when the size of the system to solve is large. However. evaluating by a simulation the probability of occurrence of very rare events means playing a very large number of histories of the system, which leads to unacceptable computing time. Highly efficient Monte Carlo should he worked out. In this paper, based on the integral equation describing state transitions of Markov dynamic system, a uniform Monte Carlo for estimating unavailability is presented. Using free-flight estimator, direct statistical estimation Monte Carlo is achieved. Using both free flight estimator and biased probability space of sampling, weighted statistical estimation Monte Carlo is also achieved. Five Monte Carlo schemes, including crude simulation, analog simulation, statistical estimation based on crude and analog simulation, and weighted statistical estimation, are used for calculating the unavailability of a repairable Con/3/30:F system. Their efficiencies are compared with each other. The results show the weighted statistical estimation Monte Carlo has the smallest variance and the highest efficiency in very rare events simulation.
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