Abstract
The paper deals with the heterogeneous degradation process of the system with gradual and instantaneous failures. For the case when the times in the degradation stages are independent and distributed exponentially with different parameters, analytical expressions are obtained for the probability of a failure on the regeneration cycle, average time before the failure on the cycle, the average cycle length with and without failure, the average total cycle length. For the case of arbitrary distributions in highly reliable systems, where failure is a rare event, an simulation splitting algorithm is proposed to speed up the construction of regeneration cycles. The results of experiments obtained by the splitting and Monte-Carlo methods are presented and compared with analytical solutions
Highlights
Ключевыеcлова: процесс деградации; системы с отказами; вероятность отказа; редкие события; метод расщепления; регенеративный метод; неоднородный случай
For the case when the times in the degradation stages are independent and distributed exponentially with different parameters, analytical expressions are obtained for the probability of a failure on the regeneration cycle, average time until failure on the cycle, average cycle length with and without failure, average total cycle length
For the case of arbitrary distributions in highly reliable systems, where failure is a rare event, a simulation splitting algorithm is proposed to speed up the construction of regeneration cycles
Summary
Процесс деградации X является регенерирующим, начало нового цикла регенерации определяет момент перехода на стадию M : τn+1 = inf{Zi > τn : X(Zi+) = M }, где n 0, τ0 := 0, Zk – это момент перехода на стадию k 1, а длины циклов Yk = τk+1 − τk, k 1, являются н.о.р
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