First Passage and Wave Density Analysis by Means of the Computer Package CROSSREG

First passage times and intercrossing times for critical, constant or timedependent, levels are of central interest in reliability and many other engineering and statistical applications of stochastic processes. For Gaussian processes, very effective numerical algorithms can be constructed by means of Slepian models and regression approximations. A Slepian model is a process that describes the process behaviour conditioned on a level crossing. By conditioning on suitably chosen random variables one can obtain quite accurate integral expressions of low dimension, for the passage time density, simply by neglecting a small residual. The regression approximation has been systematically developed by Rychlik (1987). For an account of Slepian models and regression approximations, see Lindgren & Rychlik (1991). CROSSREG is a package of FORTRAN subroutines, which perform intelligent transformation and numerical integration in regression aprroximations in order to produce high accuracy approximations of the density of first passage and intercrossing times; see Rychlik & Lindgren (1990).

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