Uncertainty Analysis for Time- and Space-Dependent Responses With Random Variables

The performance of a product varies with respect to time and space if the associated limit-state function is a function of time and space. This study develops an uncertainty analysis method that quantifies the effect of random input variables on the performance (response) over time and space. The first order reliability method (FORM) is used to approximate the extreme value of the response with respect to space at discretized instants of time. Then the response becomes a Gaussian stochastic process that is fully defined by the mean, variance, and autocorrelation functions obtained from FORM, where a sequential single loop procedure is performed for spatial and random variables. The method is successfully applied to the reliability analysis of a crank-slider mechanism, which operates in a specified period of time and space.