The estimation of failure probabilities as a false optimization problem

• A new approach to the estimation of failure probabilities is introduced.
• False optimization means finding of a minimum known in advance.
• The optimization process yields the samples in the failure domain.
• Also, the samples can be visualized in a bidimensional plot.
• The method yields the same estimate as simple Monte Carlo with low computationalcost.

This paper introduces a new regard and a powerful method for estimating small failure probabilities. It consists in considering the reliability problem as a false constrained optimization of a function. The optimization is called false because the minimum of the function is known beforehand. However, the process of computing such a minimum yields the samples located in the failure domain as a by-product, thus allowing the computation of the failure probability in a very simple manner. An algorithm based on an ad-hoc modification of the well-known Particle Swarm Optimization technique is proposed. It is characterized by the fact that it may deliver the same value of the failure probability as simple Monte Carlo simulation. In addition, the algorithm yields a visualization of all the computed samples in bidimensional plot, from which the critical realizations of the random variables can be drawn. These are the samples that mark the boundary between the safety and failure domains and therefore constitute a highly valuable information for design and diagnosis. The excellent accuracy and low computational cost of the proposed approach are illustrated with several examples.