RICE'S FORMULA AND PALM PROBABILITIES
WITH APPLICATIONS TO STRUCTURAL RELIABILITY

Greg Spaniolo

(Under the direction of Prof. M. R. Leadbetter)

This research concerns the distributions of stochastic processes at times when another random process crosses a level. The theoretical results are related to Rice's formula (1944), which describes the intensity of level crossings by a stationary Gaussian process, and in particular to a general formulation given by Leadbetter (1966). The main theorems provide formulas for the so-called "Palm" distributions of random processes, called ``marks", at level crossings by another process. In particular the theory applies to a continuous stationary stochastic process in the case when its a.s. derivative is one of the marks considered.

The theory regarding Palm distributions has been used to describe many problems in the scientific literature, including applications, for example, to engineering, climatology, and queuing theory. To illustrate potential uses of the theory developed in this research, it is applied to the statistical modeling of structural reliability in naval architecture. Specifically this concerns extreme stress loads caused by "slamming" which can severely damage a vessel operating in heavy seas. Based on general modeling of the relevant processes, an explicit form for the Palm distribution of total stress load at slams is obtained, and applied methods are developed to assess vessel lifetime structural reliability.

November 17 2000