Structural and Multidisciplinary Optimization

, Volume 57, Issue 3, pp 913–923 | Cite as

Reliability analysis for k-out-of-n systems with shared load and dependent components

  • Tianxiao Zhang
  • Yimin Zhang
  • Xiaoping Du


Many structural systems require a minimal number of components to be operational, and predicting the reliability of such systems is a challenge because surviving components share the original system workload with higher component loads after the failure of some components. The states of all the components are also dependent. Such dependence, however, is generally neglected in many existing methods. In this study, we develop a new reliability method for systems with dependent components that share the system load equally before and after other components have failed. The components are also subjected to other loads, such as a preload. The new method is based on limit-state functions that predict the states of components, and the First Order Reliability Method is used. The advantage of the proposed method is that it can directly link the system reliability with design variables and random parameters because of the use of a physics-based approach. High accuracy is maintained with the consideration of dependent component states. Two examples are used to demonstrate the good accuracy and efficiency of the proposed method.


Reliability k-out-of-n system Limit-state function Simulation 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of Illinois at ChicagoChicagoUSA
  2. 2.Shenyang University of Chemical TechnologyShenyangChina
  3. 3.Mechanical EngineeringMissouri University of Science and TechnologyRollaUSA

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