Bayesian Reliability Estimation for Deteriorating Systems with Limited Samples Using the Maximum Entropy Approach
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 c...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2013-12-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/15/12/5492 |
| _version_ | 1798041609825157120 |
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| author | Ning-Cong Xiao Yan-Feng Li Zhonglai Wang Weiwen Peng Hong-Zhong Huang |
| author_facet | Ning-Cong Xiao Yan-Feng Li Zhonglai Wang Weiwen Peng Hong-Zhong Huang |
| author_sort | Ning-Cong Xiao |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T22:23:54Z |
| format | Article |
| id | doaj.art-906c4e06f255404c8adb5b5d7db684a9 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:23:54Z |
| publishDate | 2013-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-906c4e06f255404c8adb5b5d7db684a92022-12-22T03:59:56ZengMDPI AGEntropy1099-43002013-12-0115125492550910.3390/e15125492e15125492Bayesian Reliability Estimation for Deteriorating Systems with Limited Samples Using the Maximum Entropy ApproachNing-Cong Xiao0Yan-Feng Li1Zhonglai Wang2Weiwen Peng3Hong-Zhong Huang4School of Mechanical, Electronic, and Industrial Engineering, University of Electronic Science and Technology of China, No. 2006 Xiyuan Avenue, West Hi-Tech Zone, Chengdu 611731, Sichuan, ChinaSchool of Mechanical, Electronic, and Industrial Engineering, University of Electronic Science and Technology of China, No. 2006 Xiyuan Avenue, West Hi-Tech Zone, Chengdu 611731, Sichuan, ChinaSchool of Mechanical, Electronic, and Industrial Engineering, University of Electronic Science and Technology of China, No. 2006 Xiyuan Avenue, West Hi-Tech Zone, Chengdu 611731, Sichuan, ChinaSchool of Mechanical, Electronic, and Industrial Engineering, University of Electronic Science and Technology of China, No. 2006 Xiyuan Avenue, West Hi-Tech Zone, Chengdu 611731, Sichuan, ChinaSchool of Mechanical, Electronic, and Industrial Engineering, University of Electronic Science and Technology of China, No. 2006 Xiyuan Avenue, West Hi-Tech Zone, Chengdu 611731, Sichuan, ChinaIn 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.http://www.mdpi.com/1099-4300/15/12/5492deteriorating systemmaximum entropy methodsmall sample sizesBayesian inferencefuzzy numbers |
| spellingShingle | Ning-Cong Xiao Yan-Feng Li Zhonglai Wang Weiwen Peng Hong-Zhong Huang Bayesian Reliability Estimation for Deteriorating Systems with Limited Samples Using the Maximum Entropy Approach Entropy deteriorating system maximum entropy method small sample sizes Bayesian inference fuzzy numbers |
| title | Bayesian Reliability Estimation for Deteriorating Systems with Limited Samples Using the Maximum Entropy Approach |
| title_full | Bayesian Reliability Estimation for Deteriorating Systems with Limited Samples Using the Maximum Entropy Approach |
| title_fullStr | Bayesian Reliability Estimation for Deteriorating Systems with Limited Samples Using the Maximum Entropy Approach |
| title_full_unstemmed | Bayesian Reliability Estimation for Deteriorating Systems with Limited Samples Using the Maximum Entropy Approach |
| title_short | Bayesian Reliability Estimation for Deteriorating Systems with Limited Samples Using the Maximum Entropy Approach |
| title_sort | bayesian reliability estimation for deteriorating systems with limited samples using the maximum entropy approach |
| topic | deteriorating system maximum entropy method small sample sizes Bayesian inference fuzzy numbers |
| url | http://www.mdpi.com/1099-4300/15/12/5492 |
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