A reliability analysis method is presented for time-dependent systems under uncertainty. The system response is modeled as a parameterized random process. A double-loop optimization algorithm is used. The inner loop calculates the maximum response in time using a global-local search method, and transforms a time-dependent problem into a time-independent one. The outer loop calculates multiple most probable points (MPPs) which are commonly encountered in vibration problems. The dominant MPPs with the highest contribution to the probability of failure are identified. A niching genetic algorithm is used because of its ability to simultaneously identify multiple solutions. All potential MPPs are initially identified approximately and their location is efficiently refined using a gradient-based optimizer with local metamodels. Among all MPPs, the significant ones are identified using a correlation analysis. Approximate limit states are built at the identified MPPs, and the system failure probability is estimated using bi-modal bounds. The vibration response of a cantilever plate under random oscillating pressure load and a point load illustrates the proposed method. The finite-element model is used to calculate the response.

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