A new method for the fast simulation of models of highly dependable Markov system  

作　　者：XIAO Gang LI Zhizhong 

机构地区：[1]Department of Industrial Engineering, Tsinghua University, Beijing 100084, China Department of Industrial Engineering, Tsinghua University, Beijing 100084, China

出　　处：《Science China(Technological Sciences)》2005年第1期23-30,共8页中国科学（技术科学英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.70171029).

摘　　要：To fast evaluate the small probability that starts from the all-components-up state, the system hits the failed sets before returning to the all-components-up state, Important Sampling or Important Splitting is used commonly. In this paper, a new approach distinguished from Important Sampling and Important Splitting is presented to estimate this small probability of highly dependable Markov system. This new approach achieves variance reduction through improving the estimator itself. The new estimator is derived from the integral equation describing the state transitions of Markov system. That the variance of this estimator is less than that of naive simulation at all time is proved theoretically. Two example involved reliability models with deferred repair are used to compare the methods of RB, IGBS, SB-RBS, naive simulation, and the method presented in this paper. Results show our method has the least RE.To fast evaluate the small probability that starts from the all-components-up state, the system hits the failed sets before returning to the all-components-up state, Important Sampling or Important Splitting is used commonly. In this paper, a new approach distinguished from Important Sampling and Important Splitting is presented to estimate this small probability of highly dependable Markov system. This new approach achieves variance reduction through improving the estimator itself. The new estimator is derived from the integral equation describing the state transitions of Markov system. That the variance of this estimator is less than that of naive simulation at all time is proved theoretically. Two example involved reliability models with deferred repair are used to compare the methods of RB, IGBS, SB-RBS, naive simulation, and the method presented in this paper. Results show our method has the least RE.

关 键 词：statistical estimator  variance reduction  DEPENDABILITY measures  MARKOV system  INTEGRAL equation. 

分 类 号：TH[机械工程]