Single-loop system reliability-based design optimization using matrix-based system reliability method: Theory and applications

Tam H. Nguyen, Junho Song, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

69 Scopus citations


This paper proposes a single-loop system reliability-based design optimization (SRBDO) approach using the recently developed matrix-based system reliability (MSR) method. A single-loop method was employed to eliminate the inner-loop of SRBDO that evaluates probabilistic constraints. The MSR method enables us to compute the system failure probability and its parameter sensitivities efficiently and accurately through convenient matrix calculations. The SRBDO/MSR approach proposed in this paper is applicable to general systems including series, parallel, cut-set, and link-set system events. After a brief overview on SRBDO algorithms and the MSR method, the SRBDO/MSR approach is introduced and demonstrated by three numerical examples. The first example deals with the optimal design of a combustion engine, in which the failure is described as a series system event. In the second example, the cross-sectional areas of the members of a statically indeterminate truss structure are determined for minimum total weight with a constraint on the probability of collapse. In the third example, the redistribution of the loads caused by member failures is considered for the truss system in the second example. The results based on different optimization approaches are compared for further investigation. Monte Carlo simulation is performed in each example to confirm the accuracy of the system failure probability computed by the MSR method.

Original languageEnglish (US)
Pages (from-to)110051-1100511
Number of pages990461
JournalJournal of Mechanical Design
Issue number1
StatePublished - Jan 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design


  • Computer-aided design
  • Design optimization
  • Reliability in design
  • Risk-based design
  • Systems engineering
  • Uncertainty analysis


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