### Prediction of Pipeline Failures from Incomplete Data

This report was produced for the Urban Water Research Association of Australia, a now discontinued research program.

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Prediction of Pipeline Failures from Incomplete Data

**Report No UWRAA 145**

May 1998

**SYNOPSIS**

A method for the prediction of future numbers of failures of water mains, with particular reference to the case of incomplete data, has been developed. The method uses historical failure data and other available information on assets. The model is based on the assumption that failures follow a Poisson process and arguments are presented to support this assumption. Goodness-of-fit tests show that the model fits the data from Ringwood in the Melbourne Metropolitan region.

The expected number of failures in particular classes of assets is shown to increase, approximately, as a quadratic function of time. The slope of this curve is recommended for use as a time-dependent condition index for an asset which may used to determine critical assets for replacement.

Previously proposed failure models are briefly reviewed and shown to require full failure history for their implementation. Hence, they are not suitable for the common case of incomplete data.

A power law is assumed to relate the mean function for an asset to its time in service. The mean function is the expected number of failures up to a given time. A common power of time is assumed over all assets, but different scale factors are incorporated to allow for different properties of individual assets and of their local environments.

Estimation of the model parameters takes place in two stages, utilising both the failure times of each asset and the failure numbers of each asset, including those which have not yet failed. A statistical package which will fit Generalised Linear Models is required.

For a given asset of length l and t years, the predicted number of failures in year t + 1 is simply lλ{(t + 1)ß-tß} with standard error the square root of this expression. The estimates of ß and λ obtained from the model fitting are, of course, used in this formula. By summing such expressions over classes of assets or over geographical regions, one can predict total numbers of failures over the classes or regions on a year by year basis.

The model is demonstrated using the Ringwood data. It is seen that a value of ß close to 2 is appropriate.

The prime purpose of this work was to consider the case of incomplete data. The model was tested in this respect by progressively censoring the Ringwood data set. We conclude that the Poisson model fits reasonably well but one needs a minimum of about 20 years of data to produce a satisfactory fit.

Our experience here shows the importance of collecting appropriate data. For Ringwood, there is still some unexplained variation. This may possibly be explained by other factors not available in the data record.

It is clear that there are differences in failure rate for pipes made of different materials. Also, soil type was found to be very important. Town planning zone also has an effect which is significant but less important than soil.

Some factors, such as landslip, extremes of drought, other weather-related conditions, are transient influences in the context of a long-lived asset and are not catered for in the model developed here. The extent to which these unmodelled factors may affect failure-rate is represented in the lack-of-fit of the model.

We recommend that the data collected on each asset be, minimally, length, date laid, date of failure (repair), cause of failure, date partially or fully replaced. Failure information should be linked to specific assets as far as possible, which may require re-design of an asset data-base.

Covariate data to be recorded should include pipe material, diameter, soil type, overhead traffic category, water pressure, town planning zone, presence of ground water, and any other factors which may be thought to have a bearing on failure propensity.

Specialised software would need to be provided for in-house use of the model or outside help could be obtained if the specific skills required are not internally available.

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