### 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 language | English |
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Title of host publication | Studies in Fuzziness and Soft Computing |

Pages | 425-456 |

Number of pages | 32 |

Volume | 254 |

DOIs | |

Publication status | Published - 2010 |

### Publication series

Name | Studies in Fuzziness and Soft Computing |
---|---|

Volume | 254 |

ISSN (Print) | 14349922 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computer Science (miscellaneous)
- Computational Mathematics

### Cite this

*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

**Fuzzy random redundancy allocation problems.** / Wang, Shuming; Watada, Junzo.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Studies in Fuzziness and Soft Computing.*vol. 254, Studies in Fuzziness and Soft Computing, vol. 254, pp. 425-456. https://doi.org/10.1007/978-3-642-13935-2_20

}

TY - CHAP

T1 - Fuzzy random redundancy allocation problems

AU - Wang, Shuming

AU - Watada, Junzo

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Convergence

KW - Fuzzy random variable

KW - Genetic algorithm

KW - Parallel-series system

KW - Redundancy allocation

KW - Reliability

KW - Sensitivity

UR - http://www.scopus.com/inward/record.url?scp=77956035805&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956035805&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-13935-2_20

DO - 10.1007/978-3-642-13935-2_20

M3 - Chapter

SN - 9783642139345

VL - 254

T3 - Studies in Fuzziness and Soft Computing

SP - 425

EP - 456

BT - Studies in Fuzziness and Soft Computing

ER -