Parametric Programming Approach for a Two-Unit Repairable System With Imperfect Coverage, Reboot and Fuzzy Parameters

This paper proposes a procedure for constructing the membership functions of the system characteristics of a two-unit repairable system in which the coverage factor for an operating unit failure is possibly considered. Times to failure, and times to repair of the operating units are assumed to follo...

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Bibliographic Details
Published in:IEEE transactions on reliability 2008-09, Vol.57 (3), p.498-506
Main Authors: Ke, Jau-Chuan, Huang, Hsin-I, Lin, Chuen-Horng
Format: Article
Language:English
Subjects:
Availability
Crisps
Data mining
Exponential distribution
Failure
Fuzzy
Fuzzy logic
Fuzzy set theory
Fuzzy sets
Fuzzy systems
imperfect coverage
Mathematical analysis
Mathematical models
Mathematical programming
mean time to failure
Power system modeling
Probability
Programming
Statistics
Steady-state
Studies
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Summary:This paper proposes a procedure for constructing the membership functions of the system characteristics of a two-unit repairable system in which the coverage factor for an operating unit failure is possibly considered. Times to failure, and times to repair of the operating units are assumed to follow fuzzified exponential distributions. In addition, the recovery times, and reboot times of the failed units also follow fuzzified exponential distributions. The alpha-cut approach is used to extract the fuzzy repairable system from a family of conventional crisp intervals for the desired system characteristics, determined with a set of parametric nonlinear programs using their membership functions. Two numerical examples illustrate the practicality of the proposed approach. Because the system characteristics are governed by the membership functions, more information is provided for use by designers and practitioners. The successful extension of the parameter spaces to fuzzy environments permits the repairable system to have wider practical applications.
ISSN:0018-9529
1558-1721
DOI:10.1109/TR.2008.927703