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Entropy 2013, 15(12), 5492-5509; doi:10.3390/e15125492
Article

Bayesian Reliability Estimation for Deteriorating Systems with Limited Samples Using the Maximum Entropy Approach

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Received: 17 October 2013 / Revised: 1 December 2013 / Accepted: 3 December 2013 / Published: 12 December 2013
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Abstract

In this paper the combinations of maximum entropy method and Bayesian inference for reliability assessment of deteriorating system is proposed. Due to various uncertainties, less data and incomplete information, system parameters usually cannot be determined precisely. These uncertainty parameters can be modeled by fuzzy sets theory and the Bayesian inference which have been proved to be useful for deteriorating systems under small sample sizes. The maximum entropy approach can be used to calculate the maximum entropy density function of uncertainty parameters more accurately for it does not need any additional information and assumptions. Finally, two optimization models are presented which can be used to determine the lower and upper bounds of systems probability of failure under vague environment conditions. Two numerical examples are investigated to demonstrate the proposed method.
Keywords: deteriorating system; maximum entropy method; small sample sizes; Bayesian inference; fuzzy numbers deteriorating system; maximum entropy method; small sample sizes; Bayesian inference; fuzzy numbers
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Xiao, N.-C.; Li, Y.-F.; Wang, Z.; Peng, W.; Huang, H.-Z. Bayesian Reliability Estimation for Deteriorating Systems with Limited Samples Using the Maximum Entropy Approach. Entropy 2013, 15, 5492-5509.

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