Influence of input PDF parameters of a model on a failure probability estimation

Critical probability estimation is of major interest in safety and reliability applications. In this article, we focus on a black-box model with multidimensional random input X and one random output Y. We consider the estimation of probability P that Y exceeds a threshold S. We assume that the random input X follows a multidimensional parametric density with parameters δ and thus the probability P will depend on the values of δ. In this paper, we analyze the sensitivity of the critical probability P to the model parameters δ. We propose a methodology that estimates Sobol indices with low computation cost. This strategy enables us to determine which statistical parameters have a great influence on the value of the probability and require a valuable determination. The last part of this article applies the proposed technique on a realistic case of missile collateral damage estimation.