The paper brings together the theory and practice of local linear kernel hazard estimation. Bandwidth selection is fully analysed, including double one-sided cross-validation that is shown to have good practical and theoretical properties. Insight is provided into the choice of the weighting function in the local linear minimization and it is pointed out that classical weighting sometimes lacks stability. A new semiparametric hazard estimator transforming the survival data before smoothing is introduced and shown to have good practical properties.

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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