Skip to main content
A Single-Loop Optimization Method for Reliability Analysis with Second Order Uncertainty
Engineering Optimization
  • Shaojun Xie
  • Baisong Pan
  • Xiaoping Du, Missouri University of Science and Technology
Reliability analysis may involve random variables and interval variables. In addition, some of the random variables may have interval distribution parameters owing to limited information. This kind of uncertainty is called second order uncertainty. This article develops an efficient reliability method for problems involving the three aforementioned types of uncertain input variables. The analysis produces the maximum and minimum reliability and is computationally demanding because two loops are needed: a reliability analysis loop with respect to random variables and an interval analysis loop for extreme responses with respect to interval variables. The first order reliability method and nonlinear optimization are used for the two loops, respectively. For computational efficiency, the two loops are combined into a single loop by treating the Karush-Kuhn-Tucker (KKT) optimal conditions of the interval analysis as constraints. Three examples are presented to demonstrate the proposed method.
Mechanical and Aerospace Engineering
Keywords and Phrases
  • Computational efficiency,
  • Nonlinear programming,
  • Optimization,
  • Random variables,
  • Reliability,
  • Structural analysis,
  • Uncertainty analysis,
  • Distribution parameters,
  • First order reliability methods,
  • KKT condition,
  • Limited information,
  • Non-linear optimization,
  • Reliability methods,
  • Second-order uncertainties,
  • Single loop optimization,
  • Reliability analysis
Document Type
Article - Journal
Document Version
File Type
© 2015 Taylor & Francis, All rights reserved.
Publication Date
Citation Information
Shaojun Xie, Baisong Pan and Xiaoping Du. "A Single-Loop Optimization Method for Reliability Analysis with Second Order Uncertainty" Engineering Optimization Vol. 47 Iss. 8 (2015) p. 1125 - 1139 ISSN: 0305215X
Available at: