Two-dimensional extreme distribution for estimating mechanism reliability under large variance

The effective estimation of the operational reliability of mechanism is a significant challenge in engineering practices,especially when the variance of uncertain factors becomes large.Addressing this challenge,a novel mechanism reliability method via a two-dimensional extreme distribution is investigated in the paper.The time-variant reliability problem for the mechanism is first transformed to the time-invariant system reliability problem by constructing the two-dimensional extreme distribution.The joint probability density functions(JPDFs),including random expansion points and extreme motion errors,are then obtained by combining the kernel density estimation(KDE)method and the copula function.Finally,a multidimensional integration is performed to calculate the system time-invariant reliability.Two cases are investigated to demonstrate the effectiveness of the presented method.