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.

中文翻译：

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大方差下机构可靠性的二维极限分布

有效地估计机构的运行可靠性是工程实践中的重大挑战，尤其是当不确定因素的方差变大时。针对这一挑战，本文研究了一种通过二维极限分布的新型机构可靠性方法。通过构造二维极限分布，将机构的时变可靠性问题首先转化为时变系统可靠性问题。然后通过结合核密度估计（KDE）方法和系函数来获得包括随机扩展点和极端运动误差的联合概率密度函数（JPDF）。最后，执行多维积分以计算系统的时不变可靠性。