Precursor-based hierarchical Bayesian approach for rare event frequency estimation: A case of oil spill accidents

Abstract Due to a scarcity of data, the estimate of the frequency of a rare event is a consistently challenging problem in probabilistic risk assessment (PRA). However, the use of precursor data has been shown to help in obtaining more accurate estimates. Moreover, the use of hyper-priors to represent prior parameters in the hierarchical Bayesian approach (HBA) generates more consistent results in comparison to the conventional Bayesian method. This study proposes a framework that uses a precursor-based HBA for rare event frequency estimation. The proposed method is demonstrated using the recent BP Deepwater Horizon accident in the Gulf of Mexico. The conventional Bayesian method is also applied to the same case study. The results show that the proposed approach is more effective with regards to the following perspectives: (a) using the HBA in the proposed framework provides an opportunity to take full advantage of the sparse data available and add information from indirect but relevant data; (b) the HBA is more sensitive to changes in precursor data than the conventional Bayesian method; and (c) using hyper-priors to represent prior parameters, the HBA is able to model the variability that can exist among different sources of data.

[1]  Vicki M. Bier,et al.  The analysis of accident precursors and near misses: Implications for risk assessment and risk management , 1990 .

[2]  Zhongxue Chen,et al.  A Bayesian Approach to Zero-Numerator Problems Using Hierarchical Models , 2008 .

[3]  Roger M. Cooke,et al.  Precursor Analysis for Offshore Oil and Gas Drilling: From Prescriptive to Risk-Informed Regulation , 2011 .

[4]  R. T. Bailey,et al.  Estimation from Zero‐Failure Data , 1997 .

[5]  Per Olaf Brett,et al.  Prevention of oil spill from shipping by modelling of dynamic risk. , 2007, Marine pollution bulletin.

[6]  Roger M. Cooke,et al.  The accident sequence precursor methodology for the European post-Seveso era , 1990 .

[7]  Philip M. Dixon,et al.  IMPROVING THE PRECISION OF ESTIMATES OF THE FREQUENCY OF RARE EVENTS , 2005 .

[8]  Curtis Smith,et al.  Bayesian inference in probabilistic risk assessment - The current state of the art , 2009, Reliab. Eng. Syst. Saf..

[9]  J. W. Minarick.  The US NRC accident sequence precursor program: Present methods and findings , 1990 .

[10]  Vicki M. Bier,et al.  The performance of precursor-based estimators for rare event frequencies , 1995 .

[11]  Yacov Y. Haimes,et al.  Cross-classified hierarchical Bayesian models for risk-based analysis of complex systems under sparse data , 2010, Reliab. Eng. Syst. Saf..

[12]  Vicki M. Bier,et al.  A Bayesian method for analyzing dependencies in precursor data , 1995 .

[13]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[14]  James W. Johnson,et al.  The US NRC's accident sequence precursor program: an overview and development of a Bayesian approach to estimate core damage frequency using precursor information , 1996 .

[15]  Rolf Skjong,et al.  Risk acceptance criterion for tanker oil spill risk reduction measures. , 2011, Marine pollution bulletin.

[16]  Nathan Siu,et al.  Bayesian parameter estimation in probabilistic risk assessment , 1998 .

[17]  Luoping Zhang,et al.  A probabilistic Risk Forecast of Accidental Oil Spills from Vessels in Luoyuan Bay, Fujian Province, PRC , 2010 .

[18]  Vicki M. Bier.  Statistical methods for the use of accident precursor data in estimating the frequency of rare events , 1993 .

[19]  G. Apostolakis,et al.  Expert Opinion and Statistical Evidence: An Application to Reactor Core Melt Frequency , 1979 .