Bayesian Reliability Estimation for Deteriorating Systems with Limited Samples Using the Maximum Entropy Approach
Ning-Cong Xiao,
Yan-Feng Li,
Zhonglai Wang,
Weiwen Peng,
Hong-Zhong Huang
Affiliations
Ning-Cong Xiao
School 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, China
Yan-Feng Li
School 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, China
Zhonglai Wang
School 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, China
Weiwen Peng
School 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, China
Hong-Zhong Huang
School 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, China
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.
