Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 465853, 11 pages
Research Article

Probabilistic Approach to System Reliability of Mechanism with Correlated Failure Models

School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004, China

Received 15 December 2011; Revised 22 February 2012; Accepted 6 March 2012

Academic Editor: Xue-Jun Xie

Copyright © 2012 Xianzhen Huang and Yimin Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, based on the kinematic accuracy theory and matrix-based system reliability analysis method, a practical method for system reliability analysis of the kinematic performance of planar linkages with correlated failure modes is proposed. The Taylor series expansion is utilized to derive a general expression of the kinematic performance errors caused by random variables. A proper limit state function (performance function) for reliability analysis of the kinematic performance of planar linkages is established. Through the reliability theory and the linear programming method the upper and lower bounds of the system reliability of planar linkages are provided. In the course of system reliability analysis, the correlation of different failure modes is considered. Finally, the practicality, efficiency, and accuracy of the proposed method are shown by a numerical example.