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Fuzzy Optimization pp 425–456Cite as

Fuzzy Random Redundancy Allocation Problems

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 254))

Abstract

Due to subjective judgement, imprecise human knowledge and perception in capturing statistical data, the real data of lifetimes in many systems are both random and fuzzy in nature. Based on the fuzzy random variables that are used to characterize the lifetimes, this paper studies the redundancy allocation problems to a fuzzy random parallel-series system.

Two fuzzy random redundancy allocation models (FR-RAM) are developed through reliability maximization and cost minimization, respectively. Some properties of the FR-RAM are obtained, where an analytical formula of reliability with convex lifetimes is derived and the sensitivity of the reliability is discussed. To solve the FR-RAMs, we first address the computation of reliability. A random simulation method based on the derived analytical formula is proposed to compute the reliability with convex lifetimes. As for the reliability with nonconvex lifetimes, the technique of fuzzy random simulation together with the discretization method of fuzzy random variable is employed to compute the reliability, and a convergence theorem of the fuzzy random simulation is proved. Subsequently, we integrate the computation approaches of the reliability and genetic algorithm (GA) to search for the approximately optimal redundancy allocation of the models. Finally, some numerical examples are provided to illustrate the feasibility of the solution algorithm and quantify its effectiveness.

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Authors and Affiliations

  1. Graduate School of Information, Production and Systems, Waseda University, 2-7 Hibikino, Wakamatsu, Kitakyushu, 808-0135, Fukuoka, Japan

    Shuming Wang & Junzo Watada

Authors
  1. Shuming Wang
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  2. Junzo Watada
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Editors and Affiliations

  1. Department of Mathemaitical and Statistical Sciences, University of Colorado Denver, PO Box 173364, 80217-3364, Colorado, Denver, USA

    Weldon A. Lodwick

  2. Systems Research Institute Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

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Wang, S., Watada, J. (2010). Fuzzy Random Redundancy Allocation Problems. In: Lodwick, W.A., Kacprzyk, J. (eds) Fuzzy Optimization. Studies in Fuzziness and Soft Computing, vol 254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13935-2_20

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  • DOI: https://doi.org/10.1007/978-3-642-13935-2_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13934-5

  • Online ISBN: 978-3-642-13935-2

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