Abstract
Abstract Many organization problems arising in reliability and risk assessment analysis (and in general in rare event probability computations) require challenging calculations of very small (10−2 to 10−6) probability values. This paper considers the distribution function D 1,N (x) of the sum of N non-negative continuous random variables and the relevant complementary distribution function, C 1,N =1−D 1,N . The numerical examples refer to the case of N independent random variables but the whole analysis is presented without this restriction. The method developed proves capable of evaluating very small probabilities with the accuracy appropriate to applications and very short computing times. Comparison with analytical results are provided for simple distributions, and an application to human reliability is demonstrated.
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