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New method for multi-state system reliability analysis based on linear algebraic representation

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  • Chenxi Liu
  • Nan Chen
  • Jianing Yang

Abstract

Multi-state system is a certain complex system with failure criteria that are not limited to “normal or failure.†During the life cycle, both the system and each component inside have different states at any time point. State transition of the whole system depends on the structure function while that of any component has a certain mechanism. To directly express state transition processes of the whole system and all components, we develop a linear algebraic representation method. Based on this method, dynamic transition can be expressed by mathematic equations, in which information of both system structure function and components transition mechanism is embedded. Furthermore, the extended multi-state dynamic fault tree is introduced to multi-state system modeling. By means of the proposed linear algebraic representation, standard operating rules for both static and dynamic gates are generated by introducing two variables that are used to determine whether the transition occurs and which state the output would convert into, respectively. Then, a Monte Carlo simulation coupled with the multi-state dynamic fault tree method is proposed to calculate the reliability indices of a multi-state system. The proposed method is then validated with a dynamic fault tree problem from a literature. Finally, the servo turret system is taken as an example for the application of the proposed method.

Suggested Citation

  • Chenxi Liu & Nan Chen & Jianing Yang, 2015. "New method for multi-state system reliability analysis based on linear algebraic representation," Journal of Risk and Reliability, , vol. 229(5), pages 469-482, October.
    • Handle: RePEc:sae:risrel:v:229:y:2015:i:5:p:469-482
    DOI: 10.1177/1748006X15582129
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    References listed on IDEAS

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    6. Durga Rao, K. & Gopika, V. & Sanyasi Rao, V.V.S. & Kushwaha, H.S. & Verma, A.K. & Srividya, A., 2009. "Dynamic fault tree analysis using Monte Carlo simulation in probabilistic safety assessment," Reliability Engineering and System Safety, Elsevier, vol. 94(4), pages 872-883.
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    1. Schäfer, Lukas & García, Sergio & Srithammavanh, Vassili, 2018. "Simplification of inclusion–exclusion on intersections of unions with application to network systems reliability," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 23-33.

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