Dependability Estimation For Non-Markov Cosecutive-K-Out-Of-N: F Repairable Systems By Restart Simulation

The reliability of consecutive-k-out-of-n: F system (or C (k, n: F) system) has aroused great interest since it was first studied by Kontoleon in 1980 [1]. The system consists of a sequence of n ordered components along a line such that the system fails if and only if at least k consecutive components in the system have failed. A list of typical applications of C (k, n: F) system was given by Yam et al. [2]. A research book by Chang et al. [3] provide rich information about C (k,n: F) system

RESTART Simulation of Non-Markov Consecutive-K-Out-of-N: F Repairable Systems

The reliability of consecutive-k-out-of-n: F repairable systems and (k−1)-step Markov dependence is studied. The model analyzed in this paper is more general than those of previous studies given that repair time and component lifetimes are random variables that follow a general distribution. The system has one repair service which adopts a priority repair rule based on system failure risk. Since crude simulation has proved to be inefficient for highly dependable systems, the RESTART method was used for the estimation of steady-state unavailability, MTBF and unreliability. Probabilities up to the order of 10−16 have been accurately estimated with little computational effort. In this method, a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of a rare event (e.g., a system failure) is higher. The main difficulty for the application of this method is to find a suitable function, called the importance function, to define the regions. Given the simplicity involved in changing some model assumptions with RESTART, the importance function used in this paper could be useful for dependability estimation of many systems