A conservative method for estimating the uncertainty for the probability of an upper-level event in a fault tree

Abstract. Aim. The aim of the paper is to construct a non-simulation method for finding the confidence interval for the probability of an upper-level event of a failure tree. Iterative Monte Carlo algorithms require very much time and computational resources, especially for large fault trees. Therefore, developing “fast” algorithms for finding uncertainty in a calculated fault tree is extremely important.

Methods. The algorithm was developed using classical methods of the probability theory, mathematical statistics and dependability theory. The mathematical foundation of the algorithm is the central limit theorem and certain properties of the dispersion of a random variable from the probability theory. To simplify calculations, the confidence interval was built on the assumption of a lognormal distribution of the failure rate estimate with a certain specified error factor. The initial information consists of a set of minimal cross-sections defined for the fault tree using specialized software tools, as well as dependability parameters of the events in each of the cross-sections. The cross-sections may contain dependent events that are part of common cause failure (ССF) groups. Various ССF accounting models, including the betafactor model, alpha-factor model, etc., can be used to calculate the probability of such events. To simplify the set of cross-sections, a program code is used that groups the cross-sections that are identical in value and meaning.

 Results. A conservative method for constructing a confidence interval for the probability of an upper-level event in a fault tree was developed. The method is not iterative and allows identifying the uncertainty of the final result for randomly-sized fault trees.

Conclusions. The algorithm for identifying the uncertainty can be used instead of the Monte Carlo method in specialized software suites that calculate fault trees.

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