Statistical analysis of structural failures of water pipes

Statistical analysis and prediction of failure rates of water distribution pipes are usually performed using parametric lifetime models. In this paper, a new probabilistic measure for the failure rate, called the 'likelihood of number of failures', is defined and formulated for cases where the pipe lifetimes follow parametric models. The resulting theoretical failure rates are time-invariant and, therefore, the parametric models would be useful only if the failure rates of water distribution pipes are stationary random processes. This paper then examines the stationarity of pipe failure rates in practice. For the water pipes in the western district of Melbourne (Australia), the failure rates are empirically calculated using a 4-year failure history, and it is observed that the distribution of empirical failure rates varies with time. In order to explain these variations, the pattern of rainfall in the region is compared with the pattern of failure rate variations, and in 70% of the times the two patterns are observed to be consistent. Two approaches are proposed to tackle the time-varying nature of pipe failure rate processes: regular updating of the parameters of lifetime models or developing a non-parametric technique for modelling of pipe failure rates.