Evaluation of failure probability under parameter epistemic uncertainty: application to aerospace system reliability assessment

This paper aims at comparing two different approaches to perform a reliability analysis in a context of uncertainties affecting probability distribution parameters. The first approach called “nested reliability approach” (NRA) is a classical double-loop-approach involving a sampling phase of the parameters and then a reliability analysis for each sampled parameter value. A second approach, called “augmented reliability approach” (ARA), requires to sample both distribution parameters and basic random variables conditional to them at the same phase and then integrate simultaneously over both domains. In this article, a numerical comparison is led. Possibilities offered by both approaches are investigated and the advantages of the ARA are illustrated through the application on two academic test-cases illustrating several numerical difficulties (low failure probability, nonlinearity of the limit-state function, correlation between input basic variables) and two real space system characterization (a launch vehicle stage fallback zone estimation and a collision probability between a space debris and a satellite estimation) for which only the ARA is tractable.