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

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Abstract

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.

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Authors and Affiliations

  1. University of Illinois at Chicago, Chicago, USA

    Tianxiao Zhang

  2. Shenyang University of Chemical Technology, Shenyang, China

    Yimin Zhang

  3. Mechanical Engineering, Missouri University of Science and Technology, 400 West 13 Street, Rolla, MO, 65409, USA

    Xiaoping Du

Authors
  1. Tianxiao Zhang
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  2. Yimin Zhang
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  3. Xiaoping Du
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Corresponding author

Correspondence to Xiaoping Du.

Appendix: Monte Carlo Simulation for k-of-of-n Systems

Appendix: Monte Carlo Simulation for k-of-of-n Systems

The Monte Carlo simulation (MCS) for a k-out-of-n system with k = n − 2 is discussed herein. The procedure is summarized below.

  1. 1)

    Input n, k, distribution types and parameters of L and X, and number of simulations Nsim.

  2. 2)

    Initialize the number of success N S  = 0.

  3. 3)

    Generate Nsim samples of system load L.

  4. 4)

    For i = 1 to Nsim by 1

  1. (a)

    Set number of component failures n F  = 0

  2. (b)

    Generate n samples of basic random variables X

  3. (c)

    Set component load shared by n components; call g(⋅) and obtain the state variables of the n components

  4. (d)

    Count the number of failures n F

  5. (e)

    If n F  = 0 (no component failure before the first load redistribution)

$$ {N}_S={N}_S+1 $$

End if.

If n F  = 1 (one component failure before the first load redistribution).

Delete the failed component.

Set component load shared by the remaining n − 1 components; call g(⋅) and obtain the state variables of the n − 1 components.

Count the number of failures nF1.

If nF1 = 0 (no failure after the first load redistribution)

$$ {N}_S={N}_S+1 $$

EndIf.

If nF1 = 1 (one component failure after the first load redistribution).

Delete the failed component.

Set component load shared by the n − 2 remaining components; call g(⋅) and obtain the state variables of the n − 2 components.

Count the number of failures nF2.

If nF2 = 0 (no failure after the first load redistribution)

$$ {N}_S={N}_S+1 $$

End if.

End if.

EndIf.

If n F  = 2 (two component failures before the first load redistribution).

Delete the two failed components.

Set component load shared by the n − 2 remaining components; call g(⋅) and obtain the state variables of the n − 2 components.

Count the number of failures nF1.

If nF1 = 0 (no failure after the second load redistribution)

$$ {N}_S={N}_S+1 $$

End if.

EndIf.

EndFor

  1. 5)

    System reliability R S  = N S /Nsim

With a sufficiently large value of Nsim, the system reliability obtained from MCS can be very accurate. It is the reason we use MCS to evaluate the accuracy of the proposed methods. MCS, however, is extremely computationally expensive because it requires a large number of limit-state function calls for highly reliable systems.

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Zhang, T., Zhang, Y. & Du, X. Reliability analysis for k-out-of-n systems with shared load and dependent components. Struct Multidisc Optim 57, 913–923 (2018). https://doi.org/10.1007/s00158-017-1893-z

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  • DOI: https://doi.org/10.1007/s00158-017-1893-z

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