New perspective on application of first-order reliability method for estimating system reliability

An efficient procedure employing the first-order reliability method (FORM) is proposed to evaluate the reliability of engineering systems governed by multiple limit state functions that are correlated due to the correlation among random variables involved in different limit state functions. It is shown that to estimate the system reliability, the FORM analysis for an individual limit state function included in the system needs to be carried out only by considering the random variables involved in the limit state function itself; the design point hereby obtained from the FORM can be mapped to the design point in the space that corresponds to all the random variables in the system. The latter is used as the basis to estimate the needed correlation coefficients among the linearized safety margins at the design points for the system reliability evaluation. The proposed procedure is applicable provided that the correlation matrix of the random variables associated with the system in the normal space is positive definite. Three system reliability examples are included to illustrate the application and efficiency of the proposed procedure.