| Summary: | The normality polynomial and multi-linear regression approaches are revisited for estimating the reliability index, its precision, and other reliability-related values for coastal and structural engineering applications. In previous studies, neither the error in the reliability estimation is mathematically defined nor the adequacy of varying the tolerance is investigated. This is addressed in the present study. First, sets of given numbers of Monte Carlo simulations are obtained for three limit state functions and probabilities of failure are computed. Then, the normality polynomial approach is applied to each set and mean errors in estimating the reliability index are obtained, together with its associated uncertainty; this is defined mathematically. The data is also used to derive design points and sensitivity factors by multi-linear regression analysis for given tolerances. Results indicate that power laws define the mean error of the reliability index and its standard deviation as a function of the number of simulations for the normality polynomial approach. Results also indicate that the multi-linear regression approach accurately predicts reliability-related values if enough simulations are performed for a given tolerance. It is concluded that the revisited approaches are a valuable option to compute reliability-associated values with reduced simulations, by accepting a quantitative precision level.
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