Abstract
Survival models can support the estimation of the resources needed for future renovations of sewer systems. They are particularly useful, when a large share of network will need renovation. This paper studies modelling sewer deterioration in a context, where data are available for pipes selected for inspections due to suspected or experienced poor condition. We compare the random survival forest and the Weibull regression for modelling survival and find that both methods yield similar results, but the random survival forest performs slightly better. We propose a method for estimating the range in which the actual network survival curve lies. We conclude that in order to reach reliable results, a life span model needs to be constructed based on a random sample of pipes, which are then consecutively inspected and in addition, censoring and left truncation need to be accounted for. The inspection data applied in this paper had been collected with the aim of finding pipes in poor condition in the network. As a result, the data were biased towards poor condition and unrepresentative in terms of pipe ages.
Highlights
The majority of the sewer systems in Finland have been built in the 1970s or after [1]
The random survival forest (RSF) and Weibull curves are similar to the Kaplan–Meier curve—the reason to why the Kaplan–Meier curve drops to 0 at the curve end is because the last observation is a single case of a pipe reaching the end of its life span
The comparison of the RSF and the Weibull models revealed that both methods yielded very similar survival curves approximately until pipe age 50, after which the two estimates diverge
Summary
The majority of the sewer systems in Finland have been built in the 1970s or after [1]. Survival models are so-called time-to-event models, which provide a means to determine the distribution of time until an event of interest occurs. They differ from some other statistical modelling methods in the respect that they account for censoring [4]. They are suitable for estimating, for example, the useful life of sewers. The methods existing for survival estimation can be divided into parametric, semi-parametric, and non-parametric categories [4]. The non-parametric models cover, Water 2019, 11, 2657; doi:10.3390/w11122657 www.mdpi.com/journal/water
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
