Modelling the failure risk for water supply networks with interval-censored data B. García-Mora a , A. Debón b , C. Santamaría a , A. Carrión b a Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Spain b Centro de Gestión de la Calidad y del Cambio, Universitat Politècnica de València, Spain article info Article history: Received 24 October 2014 Received in revised form 29 July 2015 Accepted 5 August 2015 Available online 12 August 2015 Keywords: Interval-censored data Reliability analysis Generalized non-linear model abstract In reliability, sometimes some failures are not observed at the exact moment of the occurrence. In that case it can be more convenient to approximate them by a time interval. In this study, we have used a generalized non-linear model developed for interval-censored data to treat the life time of a pipe from its time of installation until its failure. The aim of this analysis was to identify those network characteristics that may affect the risk of failure and we make an exhaustive validation of this analysis. The results indicated that certain characteristics of the network negatively affected the risk of failure of the pipe: an increase in the length and pressure of the pipes, a small diameter, some materials used in the manufacture of pipes and the traffic on the street where the pipes are located. Once the model has been correctly fitted to our data, we also provided simple tables that will allow companies to easily calculate the pipe's probability of failure in a future. & 2015 Elsevier Ltd. All rights reserved. 1. Introduction Worldwide, water supply systems (WSS) face the problem of aging infrastructures and increasing maintenance costs. The profits of drinking water supply companies and service quality for citizens depend on the reliability of the pipes. The classical reactive approach (used by most companies) is to wait until there is a failure in the network and then repair it, which is obviously not the best way to handle this essential public service from the point of view of either quality or reliability while by contrast other proactive strategies based more on prevention are required. These require information, quantitative tools, and advanced reliability modelling to evaluate and predict risks of failures to assess current and future state of the network. The need for these proactive strategies is even greater in developing countries with stronger economic restrictions than advanced countries. Thus, companies with these proactive strategies would have a clearer framework to make decisions on the diagnosis and rehabilitation of the pipes for effective prevention of failures in the network. We analyze failure data registered in a water supply network in order to evaluate the probability of pipe failure. This study also assesses and identifies those factors that may affect the risk of failure in order to better plan breakdown service. In reliability analysis, data refer to time from a well-defined time origin until the occurrence of some particular event or end-point. In this analysis, the variable of interest is the time T (in years) from the installation of the pipe (time origin) until its first failure (end-point). T is the time of the pipe until the first failure being as in the database is only recorded the only failure, no more. Possible subsequent repairs are not registered. Therefore, we consider the only registered failure as the end-point of the lifetime. In a standard analysis of the time until the occurrence of an event, failure times are known and observed exactly or right-censored. In this type of data the propor- tional hazard model [1] has been widely used. However, in some situations these failure times can occur in a given time interval as, for example, in survival analysis, where the event of interest, the relapse of a patient, occurs between two visits to the surgery (time interval). The data in this form are referred to as grouped or arbitrarily interval- censored data. In our case, we analyze failure data registered in a water supply network in order to evaluate the probability of pipe failure. For this, we have considered an observation window from the year 2000 until 2005 for the pipe failure times, a brief recorded pipe break history. This sampling scheme induces left-truncation into the data set (since failures before 2000 are not considered in the sample information) and right-censoring (for pipes that fail after 2005). Left- truncation is a common problem for water pipes' data sets. Some studies have dealt with this problem: [2] compare the risk associated with different statistical survival models applied to these same data sets of the present paper, under the assumption that left-truncation is a minimal problem and, more recently, it is used as an extended Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ress Reliability Engineering and System Safety http://dx.doi.org/10.1016/j.ress.2015.08.003 0951-8320/& 2015 Elsevier Ltd. All rights reserved. E-mail addresses: magarmo5@imm.upv.es (B. García-Mora), andeau@eio.upv.es (A. Debón), crisanna@imm.upv.es (C. Santamaría), acarrion@eio.upv.es (A. Carrión). Reliability Engineering and System Safety 144 (2015) 311–318