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
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.
