A Bayesian Approach for System Reliability Analysis With Multilevel Pass-Fail, Lifetime and Degradation Data Sets

Reliability analysis of complex systems is a critical issue in reliability engineering. Motivated by practical needs, this paper investigates a Bayesian approach for system reliability assessment and prediction with multilevel heterogeneous data sets. Two major imperatives have been handled in the proposed approach, which provides a comprehensive Bayesian framework for the integration of multilevel heterogeneous data sets. In particular, the pass-fail data, lifetime data, and degradation data at different system levels are combined coherently for system reliability analysis. This approach goes beyond the alternatives that deal with solely multilevel pass-fail or lifetime data, and presents a more practical tool for real engineering applications. In addition, the indices for reliability assessment and prediction are constructed coherently within the proposed Bayesian framework. It gives rise to a natural manner of incorporating this approach into a decision-making procedure for system operation and management. The effectiveness of the proposed approach is illustrated with reliability analysis of a navigation satellite.

[1]  Chris Jackson,et al.  Bayesian inference with overlapping data for systems with continuous life metrics , 2012, Reliab. Eng. Syst. Saf..

[2]  Shaofeng Liu,et al.  Engineering design: perspectives, challenges, and recent advances , 2009 .

[3]  M. Zubair,et al.  Reliability data update method for emergency diesel generator of Daya Bay Nuclear Power Plant , 2011 .

[4]  Jiqiang Guo,et al.  A Bayesian Model for Integrating Multiple Sources of Lifetime Information in System-Reliability Assessments , 2011 .

[5]  T. Bedford,et al.  Expert elicitation for reliable system design , 2006, 0708.0279.

[6]  Hong-Zhong Huang,et al.  An Approach to Reliability Assessment Under Degradation and Shock Process , 2011, IEEE Transactions on Reliability.

[7]  Eric R. Ziegel,et al.  System Reliability Theory: Models, Statistical Methods, and Applications , 2004, Technometrics.

[8]  Timothy G. Trucano,et al.  Toward a More Rigorous Application of Margins and Uncertainties within the Nuclear Weapons Life Cycle - A Sandia Perspective , 2007 .

[9]  I. Olkin,et al.  A Multivariate Exponential Distribution , 1967 .

[10]  C. Robert,et al.  Bayesian Modeling Using WinBUGS , 2009 .

[11]  J. Kruschke.  Doing Bayesian Data Analysis: A Tutorial with R and BUGS , 2010 .

[12]  David V. Mastran.  Incorporating Component and System Test Data into the Same Assessment: A Bayesian Approach , 1976, Oper. Res..

[13]  Sallie Keller-McNulty,et al.  Reliability for the 21st century , 2002 .

[14]  Christine M. Anderson-Cook,et al.  Opportunities and Issues in Multiple Data Type Meta-Analyses , 2009 .

[15]  Seth D. Guikema,et al.  Formulating informative, data-based priors for failure probability estimation in reliability analysis , 2007, Reliab. Eng. Syst. Saf..

[16]  J. Kruschke.  Doing Bayesian Data Analysis , 2010 .

[17]  William Q. Meeker,et al.  The Future of Industrial Statistics: A Panel Discussion , 2008, Technometrics.

[18]  Alyson G. Wilson,et al.  Information integration for complex systems , 2007, Reliab. Eng. Syst. Saf..

[19]  Adrian F. M. Smith,et al.  Bayesian computation via the gibbs sampler and related markov chain monte carlo methods (with discus , 1993 .

[20]  Jiqiang Guo,et al.  Bayesian Methods for Estimating the Reliability of Complex Systems Using Heterogeneous Multilevel Information , 2010 .

[21]  R. A. Waller,et al.  Bayesian reliability analysis of complex series/parallel systems of binomial subsystems and components , 1990 .

[22]  Hong-Zhong Huang,et al.  A Discrete Stress-Strength Interference Model With Stress Dependent Strength , 2009, IEEE Transactions on Reliability.

[23]  Alyson G. Wilson,et al.  A fully Bayesian approach for combining multilevel failure information in fault tree quantification and optimal follow-on resource allocation , 2004, Reliab. Eng. Syst. Saf..

[24]  J. Andrés Christen,et al.  A practical method for obtaining prior distributions in reliability , 2005, IEEE Transactions on Reliability.

[25]  Valen E. Johnson.  A Bayesian x2 test for goodness-of-fit , 2004 .

[26]  Alyson G. Wilson,et al.  Advances in Data Combination, Analysis and Collection for System Reliability Assessment. , 2006, 0708.0355.

[27]  Marko Čepin,et al.  Advantages and difficulties with the application of methods of probabilistic safety assessment to the power systems reliability , 2012 .

[28]  Loon Ching Tang,et al.  A Distribution-Based Systems Reliability Model Under Extreme Shocks and Natural Degradation , 2011, IEEE Transactions on Reliability.

[29]  Hongzhong Huang,et al.  Design Optimization With Discrete and Continuous Variables of Aleatory and Epistemic Uncertainties , 2009 .

[30]  Sangsik Choi,et al.  Reliability management and assessment for the electric traction system on the Korea High-Speed Train , 2010 .

[31]  Harry F. Martz,et al.  Bayesian reliability analysis of series systems of binomial subsystems and components , 1988 .

[32]  Leonardo Dueñas-Osorio,et al.  A Closed-Form Technique for the Reliability and Risk Assessment of Wind Turbine Systems , 2012 .

[33]  R. E. Barlow.  Combining Component and System Information in System Reliability Calculation , 1985 .

[34]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[35]  A Chateauneuf,et al.  Reliability analysis of screwed connections in high-speed trains, considering fatigue, corrosion, and imperfect maintenance operations , 2011 .

[36]  Hong-Zhong Huang,et al.  Bayesian reliability analysis for fuzzy lifetime data , 2006, Fuzzy Sets Syst..

[37]  Christine M. Anderson-Cook,et al.  Reliability Modeling using Both System Test and Quality Assurance Data , 2008 .

[38]  Kwok-Leung Tsui,et al.  Degradation Data Analysis Using Wiener Processes With Measurement Errors , 2013, IEEE Transactions on Reliability.

[39]  Byeng D. Youn,et al.  Bayesian reliability analysis with evolving, insufficient, and subjective data sets , 2009, DAC 2008.

[40]  Sallie Keller-McNulty,et al.  Testing the untestable: reliability in the 21st century , 2003, IEEE Trans. Reliab..

[41]  Nozer D. Singpurwalla,et al.  A Bayesian Estimation of the Reliability of Coherent Structures , 1978, Oper. Res..

[42]  Weiwen Peng,et al.  Life cycle reliability assessment of new products - A Bayesian model updating approach , 2013, Reliab. Eng. Syst. Saf..

[43]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[44]  V. E. Johnson,et al.  A hierarchical model for estimating the early reliability of complex systems , 2005, IEEE Transactions on Reliability.

[45]  Suk Joo Bae,et al.  Degradation models and implied lifetime distributions , 2007, Reliab. Eng. Syst. Saf..