Bayesian nonparametric reliability analysis for a railway system at component level

Railway system is a typical large-scale complex system with interconnected sub-systems which contain numerous components. System reliability is retained through appropriate maintenance measures and cost-effective asset management requires accurate estimation of reliability at the lowest level. However, real-life reliability data at component level of a railway system is not always available in practice, let alone complete. The component lifetime distributions from the manufacturers are often obscured and complicated by the actual usage and working environments. Reliability analysis thus calls for a suitable methodology to estimate a component lifetime under the conditions of a lack of failure data and unknown and/or mixture lifetime distributions. This paper proposes a nonparametric Bayesian approach with a Dirichlet Process Mixture Model (DPMM) to facilitate reliability analysis in a railway system. Simulation results will be given to illustrate the effectiveness of the proposed approach in lifetime estimation.

[1]  Fabio De Felice,et al.  Methodological Approach for Performing Human Reliability and Error Analysis in Railway Transportation System , 2011 .

[2]  M. Escobar.  Estimating Normal Means with a Dirichlet Process Prior , 1994 .

[3]  Michael,et al.  On a Class of Bayesian Nonparametric Estimates : I . Density Estimates , 2008 .

[4]  Makoto Akama,et al.  Bayesian analysis for the results of fatigue test using full-scale models to obtain the accurate failure probabilities of the Shinkansen vehicle axle , 2002, Reliab. Eng. Syst. Saf..

[5]  Nozer D. Singpurwalla,et al.  Reliability and risk , 2006 .

[6]  Bernard W. Silverman,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[7]  T. Ferguson.  A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[8]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[9]  L. Wolstenholme.  Reliability Modelling: A Statistical Approach , 1999 .

[10]  Kurt Hornik,et al.  The Comprehensive R Archive Network , 2012 .

[11]  Michael I. Jordan,et al.  Nonparametric empirical Bayes for the Dirichlet process mixture model , 2006, Stat. Comput..

[12]  J. I. Ansell,et al.  Practical Methods for Reliability Data Analysis , 1994 .

[13]  David P. Morton,et al.  Bayesian non-parametric simulation of hazard functions , 2009, Proceedings of the 2009 Winter Simulation Conference (WSC).

[14]  T. Hanson.  Modeling censored lifetime data using a mixture of gammas baseline , 2006 .

[15]  Subir Ghosh,et al.  Reliability and Risk: A Bayesian Perspective , 2008, Technometrics.

[16]  António Ramos Andrade,et al.  A Bayesian model to assess rail track geometry degradation through its life-cycle , 2012 .

[17]  C. Antoniak.  Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems , 1974 .

[18]  Alan E. Gelfand,et al.  A Computational Approach for Full Nonparametric Bayesian Inference Under Dirichlet Process Mixture Models , 2002 .

[19]  D. Wolfe,et al.  Nonparametric Statistical Methods. , 1974 .

[20]  A. Kottas.  Nonparametric Bayesian survival analysis using mixtures of Weibull distributions , 2006 .

[21]  Fernando A. Quintana,et al.  Nonparametric Bayesian data analysis , 2004 .

[22]  David B. Dunson,et al.  Classification with Incomplete Data Using Dirichlet Process Priors , 2010, J. Mach. Learn. Res..

[23]  C. R. Avery.  Power electronics reliability in rail traction , 1998 .

[24]  C. Robert,et al.  Estimation of Finite Mixture Distributions Through Bayesian Sampling , 1994 .

[25]  M. Escobar,et al.  Bayesian Density Estimation and Inference Using Mixtures , 1995 .

[26]  Purushottam W. Laud,et al.  A Bayesian Nonparametric Approach to Reliability , 1981 .

[27]  Tin Kin Ho,et al.  Reliability evaluations of railway power supplies by fault-tree analysis , 2007 .