^{1,a}, and Ander Gray

^{1,2,b}

^{1}Institute for Risk and Uncertainty, University of Liverpool, United Kingdom.

^{a}mda@liverpool.ac.uk

^{2}Culham Centre for Fusion Energy, United Kingdom Atomic Energy Authority, United Kingdom.

^{b}akgray@liverpool.ac.uk

The accuracy of Monte Carlo simulation methods depends on the computational effort invested in reducing the estimator variance. Typically reducing such variance requires invoking Monte Carlo with as many samples as one can afford. When the system is complex and the failure event is rare, it can be challenging to establish the correctness of the failure probability estimate. To combat this verification problem, we present an adaptation of the SIVIA algorithm (Set Inversion Via Interval Analysis) that computes rigorous bounds on the failure probability of rare events. With this method, the nonlinearity of the system and the magnitude of the failure event no longer constitute a limitation. This method can therefore be used for verification, when it is of interest to know the rigorous bounds of the very small target failure probability of complex systems, for example in benchmark problems. The method is rigorous i.e. inclusive and outside-in, so the more computational effort is invested the tighter the bounds. Because full separation is exercised between the engineering and the probability problem, the input uncertainty model can be changed without a re-evaluation of the physical function which opens avenues towards computing rigorous imprecise failure probability. For example, the reliability could be formulated without making dependency or distributional statements.