Predictions of the expected number of failures of water distribution network pipes are important to develop an optimal management strategy. A number of probabilistic pipe failure models have been proposed in the literature for this purpose. They have to be calibrated on failure records. However, common data management practices mean that replaced pipes are often absent from available data sets. This leads to a 'survival selection bias', as pipes with frequent failures are more likely to be absent from the data. To address this problem, we propose a formal statistical approach to extend the likelihood function of a pipe failure model by a replacement model. Frequentist maximum likelihood estimation or Bayesian inference can then be applied for parameter estimation. This approach is general and is not limited to a particular failure or replacement model. We implemented this approach with a Weibull-exponential failure model and a simple constant probability replacement model. Based on this distribution assumptions, we illustrated our concept with two examples. First, we used simulated data to show how replacement causes a 'survival selection bias' and how to successfully correct for it. A second example with real data illustrates how a model can be extended to consider covariables.