Bayesian Estimation of Residual Life for Weibull Distributed Products Based on the Fusion of Different Forms of Expert Information

Residual life estimation is increasingly concerned in reliability engineering. For conventional methods, problem arises when products are characterized as high reliability and small sample size. However, in practical engineering, experts can provide valuable reliability information, which can apparently improve the estimation precision of residual life and make up the above defects. In this paper, a method of residual life estimation is proposed by fusing expert information based on Bayesian theory. Usually, expert information could take different forms, including point estimation and confidence interval for the reliability, lifetime or the residual life, etc. Therefore, methods of determining prior distributions by fusing these kinds of expert information are presented, respectively. Then posterior distribution can be derived by fusing field lifetime data. Finally, both the Bayes estimate and credible interval for residual life are obtained by the proposed sample-based method. Validated by an numerical example, the proposed method in this paper is rather feasible and easy.

[1]  Sankaran Mahadevan,et al.  Reliability analysis with linguistic data: An evidential network approach , 2017, Reliab. Eng. Syst. Saf..

[2]  Brigitte Chebel-Morello,et al.  Accurate bearing remaining useful life prediction based on Weibull distribution and artificial neural network , 2015 .

[3]  Luis Ferreira,et al.  Parameter estimation for Weibull distribution with right censored data using EM algorithm , 2017 .

[4]  Zhaojun Li,et al.  System reliability assessment with multilevel information using the Bayesian melding method , 2018, Reliab. Eng. Syst. Saf..

[5]  Zhaojun Li,et al.  A Bayesian approach for integrating multilevel priors and data for aerospace system reliability assessment , 2017 .

[6]  Muhammad Akram,et al.  Comparison of Estimators of the Weibull Distribution , 2012 .

[7]  Enrico Zio,et al.  Development of a Bayesian multi-state degradation model for up-to-date reliability estimations of working industrial components , 2017, Reliab. Eng. Syst. Saf..

[8]  Simme Douwe Flapper,et al.  Condition-based maintenance for complex systems based on current component status and Bayesian updating of component reliability , 2017, Reliab. Eng. Syst. Saf..

[9]  Burak Birgören,et al.  Confidence interval estimation of Weibull lower percentiles in small samples via Bayesian inference , 2017 .

[10]  Debanjan Mitra,et al.  Bayesian inference of Weibull distribution based on left truncated and right censored data , 2016, Comput. Stat. Data Anal..

[11]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[12]  Yuehua Cheng,et al.  Dynamic Long Short-Term Memory Neural-Network- Based Indirect Remaining-Useful-Life Prognosis for Satellite Lithium-Ion Battery , 2018, Applied Sciences.

[13]  F. Coolen,et al.  Mean residual life of coherent systems consisting of multiple types of dependent components , 2018 .

[14]  Gianpaolo Pulcini,et al.  Early inference on reliability of upgraded automotive components by using past data and technical information , 2009 .

[15]  Binbin Xu,et al.  Bayesian reliability modeling and assessment solution for NC machine tools under small-sample data , 2015 .

[16]  Kirsten Tracht,et al.  Integration of Expert Judgment into Remaining Useful Lifetime Prediction of Components , 2014 .