Abstract:
A hierarchical Bayesian model was developed to model the occurrence of pipe failures within a water pipe network. The Bayesian methodology has several advantages over previous methods including: it does not rely heavily on the availability of failure data, it encapsulates engineering knowledge in the form of priors, it provides formal measurements of uncertainty, and it allows for the estimation of individual pipe failure rates. Further, the hierarchical nature of the model exploits similarities between pipes across a network to improve the precision of estimated parameters. A method of eliciting engineering knowledge was also developed to encapsulate engineering knowledge in a formal manner. The theoretical hierarchical Bayesian model described above was solved utilising recently developed Monte Carlo Markov chain (MCMC) sampling techniques, and integrated into a C++ object orientated discrete event simulation framework. Individual pipe failure rates were modelled using a proportional intensity power law model. The resultant 'Bayesian Simulation System' software was applied to a variety of test and 'real' problems, demonstrating the adapting and learning nature of the Bayesian methodology. In particular, the software was applied to the Howick Pressure Zone using ten years of collected failure data combined with prior information, in the form of engineering knowledge. The model proved to be robust and produced plausible estimates for all parameters. A pipe replacement policy was developed utilising the above hierarchical Bayesian formulation. The policy chooses an individual pipe replacement age utilising the current state of knowledge - prior information and data at hand. The policy was demonstrated and applied using the Bayesian Simulation System software.
