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Time-dependent reliability (TDR) is the possibility that a structure under consideration can perform the intended function under specified service conditions over a given time instant under fuzzy uncertainty . This paper is mainly concerned to identify failure modes of structures, generating the membership function of the input variables and output quantities that possess fuzziness, evaluating the time-variant performance level of failure modes, estimating the possibility safety index, and finally, evaluating the TDR of the structures. The type of uncertainty defines the method of reliability analysis, i.e., random uncertainty possesses a probabilistic approach, whereas fuzzy uncertainty leads to a possibilistic approach. Thus, to evaluate TDR, a possibilistic approach has been considered. The TDR analysis of the structures subjected to sustained load and corrosion based on probability theory is well developed. This paper significantly estimates the TDR of structures subjected to the combined effects of sustained load, corrosion, creep, and shrinkage based on possibility theory. However, it requires a rigorous procedure, a single-loop optimization method (SLOM) is employed to estimate the possibility safety index (PSI) that helps to evaluate the TDR of structures involving epistemic uncertainty. To enhance the validation of the proposed approach, several examples are exhaustively carried out that indicate the SLOM is a little conservative compared with SORM Tvedt’s algorithm in such a way that their maximum-recorded percentage difference is 9.24%.
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