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,

ISSN 0281-1944

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