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Abstract In multivariate reliability problems, which depend on one or more parameters τ, a sensitivity factor αEτ is defined as the derivative of the equivalent reliability index βE(τ)=−φ−1P f (τ) with P f (τ) the failure probability. αEτ expresses the change of αE(τ) due to small variations of τ. Since the numerical evaluation of αEτ is usually impractical, an approximation αEτ≈ατ is derived, which is asymptotically exact for extreme reliability levels. Simple formulae for ατ are given. The approximation αEτ:aτ also provides the basis for a better understanding of the commonly used alpha values αi=−1/βu i∗ as importance measures for stochastic variables.
Hohenbichler et al. (Mon,) studied this question.