Time-Variant Reliability for Non-Stationary Processes by the Outcrossing Approach

Whereas theory and concepts for the computation of time-invariant reliability are now well—known and can be performed efficiently and reliably by various methods, much less theory is available for methods which are capable of handling time variant reliability problems. Time variant problems are usually present with time—variant environmental loading and possibly time—variant (deteriorating) structural properties. One needs to compute not primarily the probability that a structural system is in an adverse state at any given time. It is rather the probability that such an adverse state is reached for the first time in a given reference period. There are two important cases in which computation of so—called first passage probabilities is still possible with time—invariant methods. This is when the failure criterion is related to strictly increasing cumulative damage phenomena, for example in structural fatigue. Then, the probability of survival is equal to the probability that damage has not reached a critical value at a given I time. The other case is when all variables are time—invariant except one which then can be replaced by its extreme value, but only in the stationary case.