Modeling of water main failure rates using the log-linear ROCOF and the power law process

This paper presents applications of the log-linear ROCOF and the power law process to model the failure rate and estimate the economically optimal replacement time of the individual pipes in a water distribution system. The performance of the two failure rate models is examined using the maximized log-likelihoods for different modeling approaches in which the method of observing failures differs. The optimal replacement time equations for the two models are developed by applying the methodology of Loganathan et al. (J Water Resour Plan Manage ASCE 128(4):271-279, 2002) for the case in which modified time scales are used. It was found that the log-linear ROCOF showed better performance than the power law process when the 'failure-time-based' method is used. Furthermore, the 'failure-time-based' method is proved to be superior compared to the 'failure-number-based' method for the water mains under study, implying that recording each failure time results in better modeling of the failure rate than observing failure numbers in some time intervals.