Estimating rate of occurrence of rare events with empirical bayes: A railway application

Reliability Engineering and System Safety

Volumn 92, Issue 5, 2007, Pages 619-627

  Quigley, John ^a   Bedford, Tim ^a   Walls, Lesley ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Credibility theory; Empirical Bayes; Estimation; Homogeneous Poisson process; Zero failure

Indexed keywords

FAILURE ANALYSIS; MAXIMUM LIKELIHOOD ESTIMATION; POISSON DISTRIBUTION; PROBABILITY; RAILROADS; STATISTICAL METHODS;

BAYES METHODS; CREDIBILITY THEORY; HOMOGENEOUS POISSON PROCESS;

RELIABILITY THEORY;

EID: 33846265021     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2006.02.007     Document Type: Article

References (26)

1. www.rssb.co.uk
2. Welker E, Lipow M. Estimating the exponential failure rate from data with no failure events. In: Proceedings of the RAMS 1974. New York: IEEE Press; 1974.
3. Bailey R. Estimation from zero-failure data. Risk Anal 17 (1997) 375-380
4. Buhlmann H. Experience rating and credibility. ASTIN Bull 4 (1967) 199-207
5. Klugman S., Panjer H., and Willmot G. Loss models: from data to decisions (1997), Wiley, New York
6. Martz H., and Waller R. Bayesian reliability analysis (1991), Krieger, New York
7. Vesely W.E., Uryasev S.P., and Samanta P.K. Failure of emergency diesel generators: a population analysis using empirical bayes methods. Reliability Eng Syst Saf 46 (1994) 221-229
8. Vaurio J.K. Uncertainties and quantification of common cause failure rates and probabilities for system analyses. Reliability Eng Syst Saf 90 (2005) 86-195
9. Vaurio J.K. Extensions of the uncertainty quantification of common cause failure rates. Reliability Eng Syst Saf 78 (2002) 63-69
10. Ferdous J., Borhan Uddin M., and Pandey M. Reliability estimation with weibull inter failure times. Reliability Eng Syst Saf 50 (1995) 285-296
11. Grabski F., and Sarhan A. Empirical Bayes estimation in the case of exponential reliability. Reliability Eng Syst Saf 53 (1996) 105-113
12. Vaurio J.K., and Jankala K.E. Evaluatin and comparison of estimation methods for failure rates and probabilities. Reliability Eng Syst Saf 91 (2006) 209-221
13. Sohn S.Y. Robust parameter design for integrated circuit fabrication procedure with respect to categorical characteristic. Reliability Eng Syst Saf 66 (1999) 253-260
14. Greenwood M., and Yule G.U. An inquiry into the nature of frequency distributions representative of multiple happening with particular reference to the occurrence of multiple attacks of disease or of repeated accidents. J R Stat Soc A 83 (1920) 255-279
15. Johnson N., Kotz S., and Kemp A. Univariate discrete distributions. 2nd Ed (1993), Wiley, New York
16. Arnold S. Mathematical statistics (1990), Prentice-Hall, New Jersey
17. Deeley J., and Lindley D. Bayes empirical Bayes. JASA 76 (1981) 833-841
18. Lawless J. Statistical models and methods for lifetime data. 2nd Ed (2003), Wiley, New York
19. Hora S., and Iman R. Bayesian analysis of learning in risk analysis. Technometrics 29 (1987) 221-228
20. Pörn K. On empirical Bayesian inference applied to poisson probability models. Linköping Studies in Science and Technology, Dissertation no 234, Linköping, 1990.
21. Bunea C. Mathematical models for reliability data. Doctoral disseration, TU Deft Netherlands, 2003.
22. Carlin B., and Louis T. Bayes and empirical Bayes methods for data analysis. 2nd Ed (2000), Chapman & Hall/CRC, London
23. Morris C. Natural exponential families with quadratic variance functions: Statistical theory. Ann Stat 11 (1983) 515-529
24. Tomberlin T. Predicting accident frequencies for drivers classified by two factors. JASA 83 (1988) 309-321
25. Maritz J., and Lwin T. Empirical Bayes methods. 2nd Ed (1989), Chapman & Hall, London
26. Knight K. Mathematical statistics (2000), Chapman and Hall, London