Evaluation of the Reliability of a Water Supply Network from Right-Censored and Left-Truncated Break Data

In this paper, we analyze failure data registered in a water supply network in order to evaluate the pipes failure probability. Only failures in normal operation conditions have been considered, excluding those caused by abnormal events. We consider an observation window from year 2000 until 2005, although the life of some of the water pipes started far in the past. This sampling scheme induces left-truncation into the data set (since failures before 2000 are not considered into the sample information) and right-censoring (for pipes that fail after 2005). We used an extended version of the Nelson–Aalen estimator, modified in order to accommodate left-truncation besides right-censoring (LTRC). Influencing factors on water pipes survival are identified. By the use of a semiparametric model based on the Cox proportional hazards model, also adapted to manage left-truncated and right-censored data, the effect of each factor over the failure risk of a pipe section has been estimated.