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Bayesian system reliability and availability analysis under the vague environment based on Exponential distribution

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Author(s): Ramin Gholizadeh | Aliakbar M. Shirazi | Maghdoode Hadian

Journal: International Journal on Soft Computing
ISSN 2229-7103

Volume: 3;
Issue: 1;
Start page: 25;
Date: 2012;
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Keywords: Bayes point estimators | Vague environment | Nonlinear programming | System reliability | System availability | Exponential distribution | Precautionary loss function.

ABSTRACT
Reliability modeling is the most important discipline of reliable engineering. The main purpose of this paper is to provide a methodology for discussing the vague environment. Actually we discuss on Bayesian system reliability and availability analysis on the vague environment based on Exponential distribution under squared error symmetric and precautionary asymmetric loss functions. In order to apply the Bayesian approach, model parameters are assumed to be vague random variables with vague prior distributions. This approach will be used to create the vague Bayes estimate of system reliability andavailability by introducing and applying a theorem called “Resolution Identity” for vague sets. For this purpose, the original problem is transformed into a nonlinear programming problem which is then divided up into eight subproblems to simplify computations. Finally, the results obtained for the subproblems can be used to determine the membership functions of the vague Bayes estimate of system reliability. Finally, the sub problems can be solved by using any commercial optimizers, e.g. GAMS or LINGO.

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