Abstract
The development of new catastrophe theory methods, coupled with probability theory is opening new possibilities to estimate the reliability measures. A brief review of the cusp catastrophe is presented in the introduction. The second part is devoted to probability approach. Manage variables are viewed as stationary random processes (functions) and a problem of overshoot of random function is formulated. Mean number of zero crossings by Gaussian random stationary process is evaluated; analytical equations to estimate the reliability function are obtained.
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