Engineering systems are usually subjected to time-variant loads and operate under time-dependent uncertainty; system performances are therefore time-dependent. Accurate and efficient estimate of system reliability is crucial for decision makings on system design, lifetime cost estimate, maintenance strategy, etc. Although significant progresses have been made in time-independent reliability analysis for components and systems, time-dependent system reliability methodologies are still limited. This dissertation is motivated by the need of accurate and effective reliability prediction for engineering systems under time-dependent uncertainty. Based on the classic First and Second Order Reliability Method (FORM and SORM), a system reliability method is developed for multidisciplinary systems involving stationary stochastic processes. A dependent Kriging method is also developed for general components. This method accounts for dependent responses from surrogate models and is therefore more accurate than existing Kriging Monte Carlo simulation methods that neglect the dependence between responses. The extension of the dependent Kriging method to systems is also a contribution of this dissertation. To overcome the difficulty of obtaining extreme value distributions and get rid of global optimization with a double-loop procedure, a Kriging surrogate modeling method is also proposed. This method provides a new perspective of surrogate modeling for time-dependent systems and is applicable to general systems having random variables, time, and stochastic processes. The proposed methods are evaluated through a wide range of engineering systems, including a compound cylinders system, a liquid hydrogen fuel tank, function generator mechanisms, slider-crank mechanisms, and a Daniels system --Abstract, page iv
