Statistical property of threshold-crossing for zero-mean-valued, narrow-banded Gaussian processes (Q5947720)

In the context of threshold-crossing of stochastic processes (that include zero-mean-valued computation), and narrow-banded Gaussian processes (for various engineering problems such as threshold-crossing probability, average number of crossing events per unit time, mean threshold-crossing duration and amplitude), the present paper obtains several results that can be summarized as follows: (a) The paper presents a new and simple numerical procedure for the efficient evaluation of threshold-crossing duration. (b) The author defines a new dimensionless parameter, called threshold-crossing intensity, in order to measure the threshold-crossing severity. The threshold-crossing intensity is equal to the ratio of the product of average number of crossing events per unit time and mean threshold-crossing duration and amplitude, over the threshold. (c) The computational results for various combinations of stochastic processes and different thresholds, the paper succeeds to establish a one-to-one relationship of two dimensionless parameters: threshold-crossing intensity and crossing probability. This new relationship can be significant for practical decision making in engineering design problems, and its application could simplify the computation of various statistics.