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Mathematical Problems in Engineering
Volume 2015, Article ID 685826, 13 pages
Research Article

Parametric Sensitivity Analysis for Importance Measure on Failure Probability and Its Efficient Kriging Solution

Institute of Aircraft Reliability Engineering, Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710129, China

Received 27 May 2014; Revised 23 September 2014; Accepted 23 September 2014

Academic Editor: Shaomin Wu

Copyright © 2015 Yishang Zhang et al. 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.


The moment-independent importance measure (IM) on the failure probability is important in system reliability engineering, and it is always influenced by the distribution parameters of inputs. For the purpose of identifying the influential distribution parameters, the parametric sensitivity of IM on the failure probability based on local and global sensitivity analysis technology is proposed. Then the definitions of the parametric sensitivities of IM on the failure probability are given, and their computational formulae are derived. The parametric sensitivity finds out how the IM can be changed by varying the distribution parameters, which provides an important reference to improve or modify the reliability properties. When the sensitivity indicator is larger, the basic distribution parameter becomes more important to the IM. Meanwhile, for the issue that the computational effort of the IM and its parametric sensitivity is usually too expensive, an active learning Kriging (ALK) solution is established in this study. Two numerical examples and two engineering examples are examined to demonstrate the significance of the proposed parametric sensitivity index, as well as the efficiency and precision of the calculation method.