Statistical analysis of structural failures of water pipes

Abstract

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. NOTATIONCICL cast iron, cement-lined ENOF(nT ) expected number of failures during the nth time interval f TFF (t) probability distribution function of the time to the first failure (TFF) IFT inter-failure time LNF likelihood of number of failures NOF k (nT ) event of occurrence of k failures during the nth time interval nT an arbitrary time interval (most recent time interval in a failure prediction application) P k (nT ) probability of occurrence of NOF k (nT )-a LNF value P EMP k ðS i Þ empirical estimate of the LNF value P k during the time period S i pdf probability distribution function (for continuous random variables) pmf probability mass function (for discrete random variables) S i time period during which the LNF values are empirically estimated TFF time to the first failure occurring after the time ðn ÿ 1ÞT t f time passed from most recent failure scale parameter of a Weibull distribution probability value associated with a confidence interval half-width of a confidence interval shape parameter of a Weibull distribution

A comparative study of statistical and machine learning methods to infer causes of pipe breaks in water supply networks

“…Temperature (water temperature, soil and/or atmospheric temperature) has rarely been incorporated in pipe breaks prediction models. Another time-dependent variable is rainfall, which has an impact on soil shrink and swell (Dehghan, McManus, and Gad 2008).…”

Fuzzified Pipes Dataset to Predict Failure Rates by Hybrid SVR-PSO Algorithm

“…The resulting theoretical failure rates were time-invariant and the parametric models would be useful only if the failure rates of water distribution pipes were stationary random processes (Dehghan, McManus & Gad, 2008 Vol. 10, No.…”