An improved monte carlo method in fault tree analysis

Abstract

The Monte Carlo (MC) method is one of the most general ones in system reliability analysis, because it reflects the statistical nature of the problem. It is not restricted by type of failure models of system components, allows to capture the dynamic relationship between events and estimate the accuracy of obtained results by calculating standard error. However, it is rarely used in Fault Tree (FT) software, because a huge number of trials are required to reach a tolerable precision if the value of system probability is relatively small. Regrettably, this is the most important practical case, because nowadays highly reliable systems are ubiquitous.In the present paper we study several enhancements of the raw simulation method: variance reduction, parallel computing, and improvements based on simple preliminary information about FT structure.They are efficiently developed both for static and dynamic FTs. The effectiveness and accuracy of the improved MC method is confirmed by numerous calculations of complex industrial benchmarks.

A new reliability analysis method for repairable systems with closed‐loop feedback links

“…It should be noted that if there are multiple CLFLs or the CLFL in the system has a complex structure, then the existing GO method and FTA will lead to a large bias. The modularization is a very general simplification method in FTA, but FTA can obtain the qualitative analysis result of the system, and the quantitative analysis result of the system is obtained according to the qualitative analysis result of the system. Although the improved Monte Carlo method can reach the same accuracy as in the raw simulation, MCS only obtains the quantitative analysis result of the system. Different from them, the accurate quantitative and qualitative analysis results of the system can both be obtained by multiple GO operations by using the proposed GO method.…”

An Efficient Approximate Markov Chain Method in Dynamic Fault Tree Analysis

“…Corresponding Monte Carlo solution is 1.407E‐3 with 1E + 6 trials and corresponding 95% confidence interval 1.407E‐3 +/− 4.1E‐5. We used a simulation with variance reduction technique . It took 90 s to run the simulation using parallel computing with four CPUs.…”

“…Monte Carlo method applied directly to DFT is flexible and efficient . It can be used both for static and dynamic FT and for non‐exponential probability distribution function of basic events (BEs).…”

“…It can be improved using different techniques, for example, variance reduction. Implementation of this technique along with parallel computing allowed to resolve the problem in case of static and non‐reparable DFT. For the dynamic system with reparable components, Monte Carlo method is still time‐consuming.…”

SFRs-based numerical simulation for the reliability of highly-coupled DFTS

“…Some achievements for finding the MCSS have been made as: Liu et al [13] proposed a series of inference rules to generate the MCSS of a given DFT; Shrestha et al [20] put forward a sorting algorithm to enumerate the MCSS; Merle et al [17] presented several temporal operators and related operation rules to deduce the structure function of a DFT which finally can be reduced to the MCSS. Actually, as to numerical simulation for reliability of a system modeled by DFT, some researchers [2,9,12,25] have made prospective studies and applications. Unfortunately, such simulation-based methods are just based on different dynamic gates.…”