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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 828407, 6 pages
Research Article

Reliability Model of Mechanical Components with Dependent Failure Modes

School of Mechanical Engineering, Shenyang University of Technology, Shenyang, Liaoning 110870, China

Received 27 July 2012; Revised 15 December 2012; Accepted 17 December 2012

Academic Editor: M. Onder Efe

Copyright © 2013 Shijie Wang. 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.


A mechanical component may fail in many modes that are usually not independent. There is generally not a joint probability density function to describe these correlated failure modes. Thus, it is difficult to compute the reliability when considering the correlations between the failure modes. It is supposed that three or more failure modes arise synchronously to be a very small probability event. The relationship between ultimate state functions in different failure modes is established by utilizing linear regression method. A double integration model for reliability of mechanical components with dependent failure modes is built according to stress-strength interference model. In case of square, cube, or exponential relationship between two ultimate state functions, a linear transformation is made. An example of pin that may fail in shear fracture, bruise, or both is discussed. The reliability is compared with that obtained by using Monte Carlo method, which represents that the reliability model with dependent failure modes proposed is correct.