A Stochastic Approach for the Analysis of Dynamic Fault Trees With Spare Gates Under Probabilistic Common Cause Failures

A redundant system usually consists of primary and standby modules. The so-called spare gate is extensively used to model the dynamic behavior of redundant systems in the application of dynamic fault trees (DFTs). Several methodologies have been proposed to evaluate the reliability of DFTs containing spare gates by computing the failure probability. However, either a complex analysis or significant simulation time are usually required by such an approach. Moreover, it is difficult to compute the failure probability of a system with component failures that are not exponentially distributed. Additionally, probabilistic common cause failures (PCCFs) have been widely reported, usually occurring in a statistically dependent manner. Failure to account for the effect of PCCFs overestimates the reliability of a DFT. In this paper, stochastic computational models are proposed for an efficient analysis of spare gates and PCCFs in a DFT. Using these models, a DFT with spare gates under PCCFs can be efficiently evaluated. In the proposed stochastic approach, a signal probability is encoded as a non-Bernoulli sequence of random permutations of fixed numbers of ones and zeros. The component's failure probability is not limited to an exponential distribution, thus this approach is applicable to a DFT analysis in a general case. Several case studies are evaluated to show the accuracy and efficiency of the proposed approach, compared to both an analytical approach and Monte Carlo (MC) simulation.