A unified framework for local sensitivity analysis of probability of failure

Resumo

In this work we present a unified framework for sensitivity analysis of probability of failure with respect
to design variables (i.e. local sensitivity). Local sensitivity analysis is generally classified in two cases. In first
case, the design variables do not affect the probability distribution. In the second case, the design variables do
affect the probability distribution (e.g. expected values). Equations for sensitivity analysis for each one of these
two cases were developed in the past. However, in this work we demonstrate that the first case (i.e design variables
that do not affect the probability distribution) can be viewed as a limit of the second case (i.e. design variables that
affect the probability distribution). This unifies the theoretical background of the problem and leads to a single set
of equations for both cases. This development is important from the theoretical point of view, since it allows an
easier mathematical analysis of the problem. From the computational point of view, it demonstrates how routines
developed to address the second case (i.e. design variables that affect the probability distribution) can be adapted
to address the first case (i.e design variables that do not affect the probability distribution).