МЕТОД ОЦЕНКИ ВЕРОЯТНОСТИ КАТАСТРОФЫ СБОРКИ ДЛЯ СЛУЧАЯ, КОГДА УПРАВЛЯЮЩИЕ ПАРАМЕТРЫ ЯВЛЯЮТСЯ СЛУЧАЙНЫМИ ФУНКЦИЯМИ

This paper deals with the estimation reliability measures from the point of catastrophe theory. An introduction to the catastrophe theory is presented, cusp catastrophe is considered and analysis of control parameters critical values is carried out at the fi rst part of the paper. Control parameters are viewed as stationary random processes (functions) and problem of overshoot of random function is formulated. Mean number of zero crossings by random stationary process was evaluated at the next stage of the research. Analytical equations can be applied for defi nition of reliability function, failure probability (cusp catastrophe probability), mean operating time to failure. The statistical linearization method used for determination of random process characteristics (mean value, dispersion). Statistical analysis of balance near critical points can be carried out by this approach. These expressions can be applied for estimation of reliability function of machines and equipment construction elements from a perspective of catastrophe theory.