Predictionof Pipeline Failures from Incomplete Data

ReportNo WSAA 145

May 1998

EXICUTIVESUMMARY

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}

with standard error the square root ofthis expression. The estimates of ßand λ obtained from the model fitting are, ofcourse, used in this formula. By summing such expressions over classes ofassets or over geographical regions, one can predict total numbers of failuresover the classes or regions on a year by year basis.

The model is demonstrated using theRingwood data. It is seen that a value of ßclose to 2 is appropriate.

The prime purpose of this work was toconsider the case of incomplete data. The model was tested in this respect byprogressively censoring the Ringwood data set. We conclude that the Poissonmodel fits reasonably well but one needs a minimum of about 20 years of data toproduce a satisfactory fit.

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

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

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

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

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

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

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