A Robust Bayesian Approach to an Optimal Replacement Policy for Gas Pipelines

In the paper, we address Bayesian sensitivity issues when integrating experts’ judgments with available historical data in a case study about strategies for the preventive maintenance of low-pressure cast iron pipelines in an urban gas distribution network. We are interested in replacement priorities, as determined by the failure rates of pipelines deployed under different conditions. We relax the assumptions, made in previous papers, about the prior distributions on the failure rates and study changes in replacement priorities under different choices of generalized moment-constrained classes of priors. We focus on the set of non-dominated actions, and among them, we propose the least sensitive action as the optimal choice to rank different classes of pipelines, providing a sound approach to the sensitivity problem. Moreover, we are also interested in determining which classes have a failure rate exceeding a given acceptable value, considered as the threshold determining no need for replacement. Graphical tools are introduced to help decisionmakers to determine if pipelines are to be replaced and the corresponding priorities.

[1]  Alfonso Suárez-Llorens,et al.  The Non Dominated Set in Bayesian Decision Problems with Convex Loss Functions , 2006 .

[2]  J. Berger,et al.  Ranges of posterior measures for priors with unimodal contaminations , 1989 .

[3]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[4]  David Ríos Insua,et al.  Robust Bayesian analysis , 2000 .

[5]  Rob J Hyndman,et al.  Sample Quantiles in Statistical Packages , 1996 .

[6]  F. Ruggeri,et al.  Robust Bayesian analysis under generalized moments conditions , 1994 .

[7]  M. R. Leadbetter.  Poisson Processes , 2011, International Encyclopedia of Statistical Science.

[8]  Fabrizio Ruggeri,et al.  ISSUES IN BAYESIAN LOSS ROBUSTNESS , 1998 .

[9]  W. J. Studden,et al.  Robust Bayesian Experimental Designs in Normal Linear Models , 1991 .

[10]  Judith Rousseau,et al.  Combining expert opinions in prior elicitation , 2010 .

[11]  Franco Caron,et al.  Sensitivity of Replacement Priorities for Gas Pipeline Maintenance , 2000 .

[12]  Francisco Javier Girón González-Torre,et al.  Quasi-Bayesian behaviour: a more realistic approach to decision making? , 1980 .

[13]  F. Ruggeri.  Posterior ranges of functions of parameters under priors with specified quantiles , 1990 .

[14]  B. Vidakovic.  Γ-Minimax: A Paradigm for Conservative Robust Bayesians , 2000 .

[15]  Alessandra Guglielmi,et al.  Methods for global prior robustness under generalized moment conditions , 2000 .

[16]  U. Makov.  Some aspects of Bayesian loss-robustness , 1994 .

[17]  Simon French,et al.  Statistical Decision Theory , 1980 .

[18]  Brani Vidakovic,et al.  Some Results on Posterior Regret ?-minimax Estima- Tion , 1993 .

[19]  Anirban DasGupta,et al.  Diameter and Volume Minimizing Confidence Sets in Bayes and Classical Problems , 1991 .

[20]  Siva Sivaganesan,et al.  On a Global Sensitivity Measure for Bayesian Inference , 2007 .

[21]  Jacinto Martín,et al.  Optimal actions in problems with convex loss functions , 2009, Int. J. Approx. Reason..

[22]  Thomas L. Saaty,et al.  The analytic hierarchy process : planning, priority setting, resource allocation , 1980 .

[23]  L. Wasserman.  A Robust Bayesian Interpretation of Likelihood Regions , 1989 .

[24]  E. Moreno.  Global Bayesian Robustness for Some Classes of Prior Distributions , 2000 .

[25]  K. Dipak,et al.  A BAYESIAN APPROACH TO LOSS ROBUSTNESS , 1998 .

[26]  Enrico Cagno,et al.  Using AHP in determining the prior distributions on gas pipeline failures in a robust Bayesian approach , 2000, Reliab. Eng. Syst. Saf..

[27]  Siva Sivaganesan,et al.  SENSITIVITY OF POSTERIOR MEAN TO UNIMODALITY PRESERVING CONTAMINATIONS , 1989 .

[28]  James O. Berger,et al.  An overview of robust Bayesian analysis , 1994 .