On some reliability applications of Rice formula for the intensity of level
crossings
Igor Rychlik
Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,
1998
ISSN 02811944
ISRN LUNFD6/NFMS3193SE

Abstract:

Let X be a stationary process with absolutely continuous sample paths.
It is shown that if E[X(0)] is finite
and if the distribution of X(0) is absolutely
continuous, then, for almost all u, the expected number of times
the process takes the value u in the unit interval is equal to the
expected number of times it crosses u, and both of them are given
by the Rice formula. The result is extended to marked crossings, then applied
in three engineering problems; in computing the average stress at slams,
in fatigue of metals and in significant sea waves analysis.


Key words:

level crossings, Rice formula, functions of finite variation, rainflow damage,
significant wave height, stress at slams