Assessment of reliability intervals under input distributions with uncertain parameters

Structural and mechanical reliability analysis often face the problem that probability distributions of the input variables are known with imprecision. This latter is normally specified by intervals of variation of their parameters. Leaving aside a crude Monte Carlo simulation consisting this case in estimating the failure probability for several sets of random realizations of the input distributions, there are no parsimonious methods for solving this problem in the general case of several interval parameters per distribution. In this paper a method intended to fill this gap is proposed. It is based on a property of the reliability plot recently proposed by the author [Hurtado, Dimensionality reduction and visualization of structural reliability problems using polar features. Probabilistic Engineering Mechanics, 29 (2012) 16–31], namely the fact that the order statistics of any function of the input random variables, used for building a limit state function, is concealed in the plot. This property, which is demonstrated herein, is used for the development of numerical methods for interval or reliability analysis, as well as for their combination for the estimation of the reliability interval. The ordering property of the plot assures that the lowest and largest values of the failure probability derives from samples contained in two small sets of realizations of the input distribution parameters located in specific plot sectors. The application of the proposed methodology is illustrated with examples that demonstrate its rigorousness, simplicity and accuracy.

► A method for reliability analysis with uncertain distributions is proposed.
► The number of parameters per distribution is unrestricted.
► Numerical methods for interval and reliability analysis on the reliability plot are proposed.
► The samples for estimating the reliability bounds are easily selected from the plot.
► SORM approximations are used for defining sample selection equations.