# 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 language English Studies in Fuzziness and Soft Computing 425-456 32 254 https://doi.org/10.1007/978-3-642-13935-2_20 Published - 2010

### Publication series

Name Studies in Fuzziness and Soft Computing 254 14349922

### Fingerprint

Redundancy
Fuzzy Random Variable
Random variables
Cost Minimization
Series System
Discretization Method
Random access storage
Parallel Systems
Convergence Theorem
Simulation Methods
Simulation
Quantify
Genetic algorithms
Integrate
Genetic Algorithm
Model
Numerical Examples
Costs

### 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

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

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

Studies in Fuzziness and Soft Computing. Vol. 254 2010. p. 425-456 (Studies in Fuzziness and Soft Computing; Vol. 254).

Research output: Chapter in Book/Report/Conference proceedingChapter

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