This work is concerned with the time-dependent mechanism reliability defined over a period of time where a certain motion output is required. An envelope approach is proposed to improve the accuracy of the time-dependent mechanism reliability analysis. The envelope function of the motion error over the time period is created. Since the envelope function is not explicitly related to time, the time-dependent problem is converted into a time-independent problem. Then the envelope function is approximated by piecewise hyper-planes. To find the expansion points of the hyper-planes, the approach linearizes the motion error at the means of random dimension variables, and this approximation is accurate because the tolerances or the variances of the dimension variables are small. Then the expansion points are found with the maximum probability density at the failure threshold. The time-dependent mechanism reliability is then estimated by a multivariable normal distribution function at the expansion points. As an example, analytical equations are derived for a four-bar function generating mechanism. The numerical example shows the significant accuracy improvement.

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