Time-variant reliability analysis using phase-type distribution-based methods

The performance of engineering structures often varies over time due to the randomness and time variability of material properties, environmental conditions and load effects. This paper proposes phase-type (PH) distribution-based methods for efficient time-variant reliability analysis. The core of the proposed methods is to approximate the extreme value of a stochastic process as a PH distributed random variable, and treat the time parameter as a uniformly distributed variable. Consequently, the time-variant reliability problem is transformed into a time-invariant one. Three representative time-invariant reliability methods, first-order reliability method (FORM), importance sampling (IS) and adaptive Kriging (AK) surrogate model-based IS method (AK-IS), are integrated with the PH distribution-based approximation strategy to form the proposed methods, namely PH-FORM, PH-IS and PH-AKIS. The efficiency and accuracy of these methods are demonstrated through three examples. All codes in the study are implemented in MATLAB and provided as supplementary materials.