Eawag, Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland.
Water Res. 2013 Jul 1;47(11):3696-705. doi: 10.1016/j.watres.2013.04.017. Epub 2013 Apr 22.
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.
预测供水管网管道的失效数量对于制定最佳管理策略非常重要。为此，文献中提出了许多概率性管道失效模型。这些模型需要根据失效记录进行校准。然而，常见的数据管理实践意味着，更换的管道往往不在可用数据集内。这导致了“生存选择偏差”，因为经常失效的管道更有可能从数据中缺失。为了解决这个问题，我们提出了一种正式的统计方法，通过替换模型扩展管道失效模型的似然函数。然后可以应用频率论最大似然估计或贝叶斯推断进行参数估计。这种方法是通用的，不限于特定的失效或替换模型。我们使用威布尔-指数失效模型和简单的常数概率替换模型实现了这种方法。基于这种分布假设，我们用两个示例说明了我们的概念。首先，我们使用模拟数据展示了替换如何导致“生存选择偏差”，以及如何成功地纠正这种偏差。第二个使用真实数据的示例说明了如何扩展模型以考虑协变量。
