First passage failure: Analysis alternatives

Most mechanical and structural failures can be formulated as first passage problems. The traditional approach to first passage analysis models barrier crossings as Poisson events. The crossing rate is established and used in the Poisson framework to approximate the no-crossing probability. While this approach is accurate in a number of situations, it is desirable to develop analysis alternatives for those situations where traditional analysis is less accurate and situations where it is difficult to estimate parameters of the traditional approach. This paper develops an efficient simulation approach to first passage failure analysis. It is based on simulation of segments of complex random processes with the Karhunen-Loeve expansion, use of these simulations to estimate the parameters of a Markov chain, and use of the Markov chain to estimate the probability of first passage failure. Some numerical examples are presented.