Statistical Modelling of Pipe Failures in Water Networks

I Abstract European cities spend in the order of one billion Euros a year to rehabilitate water supply networks. Rehabilitation costs will increase in the coming decades as networks age and deteriorate. The rational behind today’s rehabilitation decisions is unclear. In the best case, decisions are based on practical experience like failure frequency. During the past 10-20 years, most of the larger European water utilities have implemented Automated Mapping/Facilities Management (AM/FM) system for recording and managing inventory and maintenance data for their distribution networks. The information registered in these systems can be used to predict future pipe failures in the network, improving network management decisions. This thesis aims to make a modest contribution to improving the prediction of pipe failures in water networks.European cities spend in the order of one billion Euros a year to rehabilitate water supply networks. Rehabilitation costs will increase in the coming decades as networks age and deteriorate. The rational behind today’s rehabilitation decisions is unclear. In the best case, decisions are based on practical experience like failure frequency. During the past 10-20 years, most of the larger European water utilities have implemented Automated Mapping/Facilities Management (AM/FM) system for recording and managing inventory and maintenance data for their distribution networks. The information registered in these systems can be used to predict future pipe failures in the network, improving network management decisions. This thesis aims to make a modest contribution to improving the prediction of pipe failures in water networks. This thesis presents an evaluation of statistical methods for modelling pipe failures for each individual pipe in a water distribution network and shows whether the existing data in Gemini VA (a Norwegian AM/FM system for waterand sewerage utilities) is sufficient input for these models. Statistical methods that are appropriate for modelling pipe failures are described, and the models are applied in a case study using data for the water distribution network in Trondheim, Norway. This thesis introduces the Non Homogeneous Poisson Process (NHPP) with covariates (i.e. explanatory variables) as an appropriate method for modelling pipe failures in water networks. The NHPP has been successfully used to model other minimal repair processes. I.e., the system is not restored to a ‘good-asnew’ state after the repair, and the intensity of failures for the repaired object is unchanged. This is the normal situation for pipe repairs in water distribution systems. As part of this research, a computer program has been developed that estimates the parameters in the NHPP (“Power law” model). The results from this NHPP model are compared to the results obtained from a modified Weibull Proportional Hazards Model (PHM), where the hazard function is allowed to continue beyond the pipe’s first failure. The statistical models have been calibrated, verified and used to predict failures for both networks (i.e. group of pipes) and individual pipes. Covariates that have a significant influence on the rate of occurrence of failures (ROCOF) are documented. Both the Weibull PHM and the NHPP are capable of modelling pipe failures. In the case study, the Weibull PHM shows a tendency to overestimate failures compared to NHPP. Model results fit the observed data best at network level, but are also satisfactory at pipe level when there is adequate calibration data. The NHPP can easily be used to predict the expected number of future failures by directly integrating the function defining the intensity of failures. The intensity function in the Weibull PHM is a step function, and can not be directly integrated. A timeconsuming Monte Carlo simulation is required to predict future failures. Based on the results from the