Fuzzy random redundancy allocation problems

Shuming Wang, Junzo Watada

    Research output: Chapter in Book/Report/Conference proceedingChapter

    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.

    Original languageEnglish
    Title of host publicationStudies in Fuzziness and Soft Computing
    Pages425-456
    Number of pages32
    Volume254
    DOIs
    Publication statusPublished - 2010

    Publication series

    NameStudies in Fuzziness and Soft Computing
    Volume254
    ISSN (Print)14349922

    Keywords

    • Convergence
    • Fuzzy random variable
    • Genetic algorithm
    • Parallel-series system
    • Redundancy allocation
    • Reliability
    • Sensitivity

    ASJC Scopus subject areas

    • Computer Science (miscellaneous)
    • Computational Mathematics

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  • Cite this

    Wang, S., & Watada, J. (2010). Fuzzy random redundancy allocation problems. In Studies in Fuzziness and Soft Computing (Vol. 254, pp. 425-456). (Studies in Fuzziness and Soft Computing; Vol. 254). https://doi.org/10.1007/978-3-642-13935-2_20