On imprecision in relation to uncertainty importance measures

Abstract : A number of uncertainty importance measures have been proposed in the literature to extend classical risk and reliability importance measures in the presence of epistemic uncertainty. Uncertainty impor-tance measures typically reflect to what degree uncertainty about risk and reliability parameters at the compo-nent level influences uncertainty about parameters at the system level. The definition of these measures is typically founded on a Bayesian perspective where subjective probabilities are used to express epistemic un-certainty; hence, they do not reflect the effect of imprecision in probability assignments, as captured by alter-native uncertainty representation frameworks such as imprecise probability, possibility theory and evidence theory. In the present paper we consider the issue of imprecision in relation to uncertainty importance meas-ures. We define an imprecision importance measure to evaluate the effect of removing imprecision - in the present paper focusing on imprecision removal to the extent that no epistemic uncertainty remains; as further work we suggest to also consider the more general case of imprecision removal to the extent that a probabilis-tic representation of uncertainty remains. A numerical example is presented to illustrate the suggested measure in the case of a possibilistic uncertainty representation.
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R. Flage, Terje Aven, Piero Baraldi, Enrico Zio. On imprecision in relation to uncertainty importance measures. ESREL 2011, Sep 2011, Troyes, France. pp.2250-2255. ⟨hal-00658103⟩

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