A new methodology for uncertainty evaluation in risk assessment. Bayesian estimation of a safety index based upon extreme values

A methodological contribution is presented in the framework of safety and security studies, where it is of paramount importance to be able to statistically characterize very rare and uncertain events. For this purpose, the paper illustrates a Bayesian methodology for the estimation of a stochastic process characterizing the maximum value of a succession of random variables (RV), representing the successive values of a disturbance in time. This stochastic process, already proposed and applied in power systems by the authors, is a powerful mathematical tool very adequate for describing a safety index (SI) for any engineering system, as discussed in the paper, also with some references to electrical applications. The paper is focused upon a Bayesian estimation (BE) technique, applied for the first time at the best of authorspsila knowledge, in which a new probability density function (pdf) -the so-called ldquoNegative Exponential Betardquo pdf - is adopted for converting prior information about rare events probabilities into accident rate information. Such BE is both efficient and easy to implement, as shown also by means of numerical simulations. In particular, the superiority of the BE with respect to the ldquoclassicalrdquo Maximum Likelihood (ML) estimation methods, traditionally adopted in power system applications, is illustrated in terms of ldquorelative efficiencypsila. The ML estimates are outperformed by the BE, especially when few experimental data are available, as typically occurs when dealing with rare events affecting safety.