**Predictionof Pipeline Failures from Incomplete Data**

**ReportNo WSAA 145**

May 1998

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**EXICUTIVESUMMARY**

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A method for theprediction of future numbers of failures of water mains, with particularreference to the case of incomplete data, has been developed. The method useshistorical failure data and other available information on assets. The model isbased on the assumption that failures follow a Poisson process and argumentsare presented to support this assumption. Goodness-of-fit tests show that themodel fits the data from Ringwood in the Melbourne Metropolitan region.

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

Previouslyproposed failure models are briefly reviewed and shown to require full failurehistory for their implementation. Hence, they are not suitable for the commoncase of incomplete data.

A power law isassumed to relate the mean function for an asset to its time in service. Themean function is the expected number of failures up to a given time. A commonpower of time is assumed over all assets, but different scale factors areincorporated to allow for different properties of individual assets and oftheir local environments.

Estimation of themodel parameters takes place in two stages, utilising both the failure times ofeach asset and the failure numbers of each asset, including those which havenot yet failed. A statistical package which will fit Generalised Linear Modelsis required.

For a given assetof length *l* and *t * years, the predictednumber of failures in year *t *+ 1 issimply

*lλ*{(*t *+ 1)^{ß}-*t*^{ß}}

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