Variance-based reliability sensitivity analysis and the FORM α-factors

In reliability assessments, it is useful to compute importance measures that provide information on the influence of the input random variables on the probability of failure. Classical importance measures are the alpha-factors, which are obtained as a by-product of the first-order reliability method (FORM). These factors are the directional cosines of the most probable failure point in an underlying independent standard normal space. Alternatively, one might assess sensitivity by a variance decomposition of the indicator function, i.e., the function that indicates membership of the random variables to the failure domain. This paper discusses the relation of the latter variance-based sensitivity measures to the FORM alpha-factors and analytically shows that there exist one-to-one relationships between them for linear limit-state functions of normal random variables. We also demonstrate that these relationships enable a good approximation of variance-based sensitivities for general reliability problems. The derived relationships shed light on the behavior of first-order and total-effect indices of the failure event in engineering reliability problems.