A new approach for measuring uncertainty importance and distributional sensitivity in probabilistic safety assessment

Abstract

The uncertainty importance and distributional sensitivity analyses provide information on the relative contribution of the input uncertainties to the output uncertainty and the relative impact on the change of the output distribution induced by various distributional changes in the inputs. A key step in performing the analyses is determination of suitable measure upon which the largest contributors and impacts to the output uncertainties are to be assessed. In this paper, a collective measure for the uncertainty importance and distributional sensitivity is presented. The new measure is based on the information theory in which the entropy is a measure of uncertainty represented by a probability density function. The measure is derived explicitly for the cases that the simulated output distributions are given by well known probability distributions. For general applications, the measure is also derived for the maximum entropy probability density function. Its feasibility in PSA is studied through an example application. For all cases, the results are compared with the existing methods. From the results of example application, it is shown that the proposed measure can be used as a useful tool for exploring changes in a risk profile due to various input uncertainties including the effect of incorporating different expert opinions. The proposed measure is a direct indicator of uncertainty importance and robustness of conclusions based on the entire output distributions.