Probability Distribution of Maximum Load Generated by Stochastic Hazards Modeled as Shock, Pulse, and Alternating Renewal Processes

Abstract

The distribution of the maximum load generated by stochastic and recurring hazards is of primary importance in structural reliability analysis. In the current literature, this distribution is estimated by either relying on the asymptotic extreme value theory or assuming that occurrences of a hazard follow the homogeneous Poisson process. However, assumptions underlying these approaches become questionable when the maximum load distribution is required for a short service life, such as in reliability assessment of temporary structures and aging infrastructure systems nearing the end of life (e.g., old nuclear plants). This paper fills this gap in the literature by presenting a more general and accurate solution for the probability distribution of the maximum load generated by stochastic hazards which can be modeled as shock, pulse, and alternating renewal processes. This work is a considerable advancement of the state of the art in probabilistic analysis of maximum value distribution.