Model:
The asset failure rate has
been modelled using a Weibull process. The predicted number of bursts E(Ni)
for the i th asset with length l km and age since
construction of t years is given by E(Ni)=liqi(tib).
The parameters to be determined in this model are the shape parameter b
and the vector of coefficients a which
appear in the model through the scale parameter, qi
= eaTxi.
The xi consist of explanatory variables, which
can include asset material, size and pressure, soil type and the amount of
overhead traffic. The shape parameter is assumed to be constant for all
assets.
Method:
Historic failure data is required to fit the model. Typically
computerised failure records are limited to recent years, giving rise to
the need to satisfactorily handle truncated data for assets with failures
before the commencement of the data collection. The above model can be
modified to account for truncated data by replacing tib
by t2ib
- t1ib
where t2i is the age of
the asset since construction and t1i
is the age of the asset since commencement of data collection. The maximum
likelihood estimates of the parameters a and
b are obtained by an iterative procedure,
alternately fitting a generalised linear model for a,
then using the bisection method to determine b
. The shape parameter typically lies between 1 and 3.
Results:
Actual and predicted failure numbers from the model are compared in
Figure 1. The solid line is the predicted number of
failures from the model, plotted against time. The points are the actual
numbers of failures for the years indicated
The predicted results include amendment for replaced assets. For this
data set, the optimum value of b was found to
be 2.3. The model has already been successfully used on data from
Australian Water Authorities.
Predictions:
A key issue for water authorities is the ongoing maintenance of their
assets. The model gives predictions of the pattern of failures and hence
of the associated repair costs. It also identifies those assets most at
risk of failure and so can be used to determine an optimal strategy of
replacement. The assets are ranked according to their value of dE(N)/dt.
On this criterion the worst k km are replaced each year. Figure 2
indicates the number of failures resulting from a strategy of annual
replacement of the worst 0 to 4 km of assets for the same data as shown in
figure 1.
Acknowledgements
This work has been done in collaboration with John Darroch (formerly
Flinders University of SA).
Main Contact
This model is currently being updated by Alan Veevers.
Contact: Alan Veevers
Ph: +61-(0)3-9545-8019 Fax: +61-(0)3-9545-8080
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