• 1
    Lai CD, Xie M. Stochastic Ageing and Dependence for Reliability. Springer: New York, 2006.
  • 2
    Singpurwalla N, Mazzuchi T, Ozekici S, Soyer R. Stochastic process models for reliability in dynamic environments. Handbook of Statistics 2003; 22:11091129.
  • 3
    Yashin AI, Manton KG. Effects of unobserved and partially observed covariate processes on system failure: a review of models and estimation strategies. Statistical Science 1997; 12:2034.
  • 4
    Kelly DL, Smith CL. Bayesian inference in probabilistic risk assessment—The current state of the art. Reliability Engineering and System Safety 2009; 94(2):628643.
  • 5
    Colombo AG, Costantini D, Jaarsma, RJ. Bayes Nonparametric Estimation of Time-dependent Failure Rate. Reliability, IEEE Transactions on 1985; 34(2):109112.
  • 6
    Ho MW. On Bayes inference for a bathtub failure rate via S-paths. Annals of the Institute of Statistical Mathematics 2011; 63:827850.
  • 7
    Berger JO. Statistical Decision Theory and Bayesian Analysis (2nd Edn). Springer: New York, 1985.
  • 8
    Krivtso V, Wasiloff J, Classical vs. Bayes reliability growth in theory and practice. 54th Annual Quality Congress Proceedings, 2000; 311316.
  • 9
    Siu NO, Kelly DL. Bayesian parameter estimation in probabilistic risk assessment, Reliability Engineering and System Safety, 1998, 62: 89116. DOI: 10.1016/S0951-8320(97)00159-2.
  • 10
    Kelly DL, Smith CL, Bayesian inference in probabilistic risk assessment – The current state of the art. Reliability Engineering and System Safety 2009; 94:628643. DOI: 10.1016/j.ress.2008.07.002.
  • 11
    Gilks WR, Richardson S, Spiegelhalter DJ. Markov Chain Monte Carlo in Practice. Chapman & Hall/CRC: London, 1996.
  • 12
    Ching WK, Michael KN. Markov Chains. Models, Algorithms and Applications. Springer: New York, 2006.
  • 13
    Lunn DJ, Thomas A, Best N, WinBUGS — a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing 2000; 10:325337. DOI: 10.1023/A:1008929526011.
  • 14
    Xie M, Lai CD. Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function. Reliability Engineering and System Safety 1995; 52:8793. DOI: 10.1016/0951-8320(95)00149-2.
  • 15
    Wolford AJ, Atwood CL, Roesener WS. Ageing Data Analysis and Risk Assessment – Development and Demonstration Study. NUREG/CR5378, 1992.
  • 16
    Atwood CL. Parametric estimation of time-dependent failure rates for probabilistic risk assessment. Reliability Engineering and System Safety 1992; 37:181194. DOI: 10.1016/0951-8320(92)90122-2.
  • 17
    Rodionov A. Application of Statistical Methods for Identification of Ageing Trends IRSN/DSR Report No. 47, 2005.
  • 18
    Okazaki T, Aldemir T. Ageing Effects on Time-Dependent Nuclear Plant Unavailability with Changing Surveillance Interval. Proceedings of International Conference PSAM 7 – ESREL'04. 2004, 15591566.
  • 19
    Radulovich RD, Vesely WE, Aldemir T. Ageing Effects on Time-Dependent Nuclear Plant Component Unavailability: an Investigation of Variations From Static Calculations // Nuclear Technology. 1995; 112:2141.
  • 20
    Chib S, Clyde M, Woodworth G, Zaslavsky A. Subjective and objective Bayesian statistics: principles, models, and applications. Wiley: New Jersey, 2003.
  • 21
    Coolen FPA. A Bayes-competing risk model for the use of expert judgment in reliability estimation. Reliability Engineering 1992; 14:107930.
  • 22
    Coolen FPA. On Bayesian reliability analysis with informative priors and censoring. Reliability Engineering and System Safety 1996; 53:9198 .
  • 23
    Gelman A, Bois F, Jiang J. Physiological pharmacokinetic analysis using population modeling and informative prior distributions. Journal of the American Statistical Association 1996; 91:14001412.
  • 24
    Guikema SD. Formulating informative, data-based priors for failure probability estimation in reliability analysis. Reliability Engineering and System Safety 2007; 92:490502.
  • 25
    Berger, JO, Bayarri, MJ. The Interplay of Bayesian and Frequentist Analysis. Statistical Science 2004; 19:5880.
  • 26
    Jeffreys H. An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 1946 186: 453461. DOI: 10.1098/rspa.1946.0056.
  • 27
    Hoeting J, Madigan D, Raftery AE, Volinsky C. Bayesian Model Averageing: A Tutorial. Statistical Science 1999; 14:382417.
  • 28
    Kulinskaya E, Morgenthaler S, Staudte RG. Meta Analysis A Guide to Calibrating and Combining Statistical Evidence. John Wiley & Sons Ltd.: West Sussex, 2008; 255281.
  • 29
    Alvin KF, Oberkampf WL, Diegert KV, Rutherford BM. Uncertainty quantification in computational structural dynamics: a new paradigm for model validation. In Proceedings of the 16th international modal analysis conference. Society for Experimental Mechanics: Santa Barbara, CA, 1998; 11911198.
  • 30
    Zhang R, Mahadevan S. Model uncertainty and Bayesian updating in reliability-based inspection. Structural Safety 2000 22:145160. DOI: 10.1016/S0167-4730(00)00005-9.
  • 31
    Park I, Amarchinta HK, Grandhi RV. A Bayesian approach for quantification of model uncertainty, Reliability Engineering and System Safety 2010; 95:777785. DOI: 10.1016/j.ress.2010.02.015.
  • 32
    Ntzoufras I, Bayesian Modelling Using WinBUGS. Wiley: New Jersey, 2009.
  • 33
    Gelman A, Meng X, Stern H, Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica 1996; 6:733807.
  • 34
    Dei DK, Rao CR. Bayesian Thinking: Modelling and Computation. Handbook of statistics vol. 25, Elsevier: North-Holland, New York, 2005.
  • 35
    Gelman A, and Meng XL, Model checking and model improvement, in Gilks W, Richardson S, Spiegelhalter D, eds., Markov Chain Monte Carlo in Practice, Chapman & Hall: Suffolk, UK, 1996, 189201.
  • 36
    Spiegelhalter D, Best N, Carlin B, van der Linde A. Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society B 2002; 64:583639. DOI: 10.111/1467-9868.00353.
  • 37
    Kelly DL, Smith C. Bayesian Inference for Probabilistic Risk Assessment: A Practitioner's Guidebook. Springer, 2011.
  • 38
    Friel N, Pettitt AN. Marginal likelihood estimation via power posteriors. Journal of Royal Statistical Society: Series B (Statistical Methodology) 2008; 70:589607.