A new phase-type distribution-based method for time-dependent system reliability analysis

It remains a grand challenge to handle time-dependent system reliability with stochastic process due to the complexity and the high computational cost. In this work, a new phase-type (PH) distribution-based method is proposed for time-dependent system reliability analysis. The PH distribution-based strategy is incorporated with the adaptive Kriging (AK) surrogate model to make up the new PH-AK method. In the PH stage, the main concern of the method is to obtain the extreme value distribution of the stochastic process, which is approximated as a random variable with PH distribution. Moreover, the time parameter is treated as a uniform random variable. Therefore, the time-dependent system reliability analysis is transformed into a time-independent one. In the AK stage, the AK surrogate model is then employed for efficient reliability analysis. And the Metropolis-Hastings algorithm is adopted for generating samples of the extreme value based on the probability density function of the PH distribution. Four examples are utilized to illustrate the effectiveness of the PH-AK method, and results show that the proposed method can efficiently and accurately analyze the time-dependent system reliability.