The paper considers the problem of representing non-Markovian systems that evolve stochastically over time. It is often necessary to use approximations in the case the system is non-Markovian. Phase type distribution ...The paper considers the problem of representing non-Markovian systems that evolve stochastically over time. It is often necessary to use approximations in the case the system is non-Markovian. Phase type distribution is by now indispensable tool in creation of stochastic system models. The paper suggests a method and software for evaluating stochastic systems approximations by Markov chains with continuous time and countable state space. The performance of a system is described in the event language used for generating the set of states and transition matrix between them. The example of a numerical model is presented.展开更多
Monte Carlo simulation has become an important tool for estimating the reliability andavailability of dynamic system, since conventional numerical methods are no longer efficient whenthe size of the system to solve is...Monte Carlo simulation has become an important tool for estimating the reliability andavailability of dynamic system, since conventional numerical methods are no longer efficient whenthe size of the system to solve is large. However, evaluating by a simulation the probability of oc-currence of very rare events means playing a very large number of histories of the system, whichleads to unacceptable computing time. Highly efficient Monte Carlo should be worked out. In thispaper, based on the integral equation describing state transitions of Markov dynamic system, a u-niform Monte Carlo for estimating unavailability is presented. Using free-flight estimator, directstatistical estimation Monte Carlo is achieved. Using both free-flight estimator and biased proba-bility space of sampling, weighted statistical estimation Monte Carlo is also achieved. Five MonteCarlo schemes, including crude simulation, analog simulation, statistical estimation based oncrude and analog simulation, and weighted statistical estimation, are used for calculating the un-availability 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 thehighest efficiency in very rare events simulation.展开更多
基金Supported by National Basic Research and Development Program of China （973 Program） （2009CB320600）, National Natural Science Foundation of China （60774004）, Taishan Scholar Construction Engineering of Shandong Government, National Natural Science Foundation for Distinguished Young Scholars of China （60825304）
文摘The paper considers the problem of representing non-Markovian systems that evolve stochastically over time. It is often necessary to use approximations in the case the system is non-Markovian. Phase type distribution is by now indispensable tool in creation of stochastic system models. The paper suggests a method and software for evaluating stochastic systems approximations by Markov chains with continuous time and countable state space. The performance of a system is described in the event language used for generating the set of states and transition matrix between them. The example of a numerical model is presented.
文摘Monte Carlo simulation has become an important tool for estimating the reliability andavailability of dynamic system, since conventional numerical methods are no longer efficient whenthe size of the system to solve is large. However, evaluating by a simulation the probability of oc-currence of very rare events means playing a very large number of histories of the system, whichleads to unacceptable computing time. Highly efficient Monte Carlo should be worked out. In thispaper, based on the integral equation describing state transitions of Markov dynamic system, a u-niform Monte Carlo for estimating unavailability is presented. Using free-flight estimator, directstatistical estimation Monte Carlo is achieved. Using both free-flight estimator and biased proba-bility space of sampling, weighted statistical estimation Monte Carlo is also achieved. Five MonteCarlo schemes, including crude simulation, analog simulation, statistical estimation based oncrude and analog simulation, and weighted statistical estimation, are used for calculating the un-availability 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 thehighest efficiency in very rare events simulation.
