*Statistical modelling can be used to forestall network asset failures in the most financially efficient way possible, says Tim Watson.*

It might be thought that using statistical models to predict the number of fish in the ocean or holes in roads is a far cry from predicting when a pipe might fail in the Scottish Highlands, but the beauty of data and statistics is that they do not know, or care, whether the subject is a fish, road or pipe: the same techniques can be applied to all.

The problem common to all such work is trying to manage resources in the most efficient and sustainable way. To do this you need some kind of statistical model of the resource, or asset, to help develop management and investment ­strategies.

Once a statistical model is built, it can be used to predict the future state of a resource given a particular management strategy. This is called scenario building, and it allows you to assess the effects that decisions may have now and in the future. Alternatively, a statistical model can be used to determine the optimal strategy given a set of constraints.

To work properly, the model must be robust and applicable to a range of uses in a repeatable and transparent manner. Then quality and unbiased data must be obtained to fit the model. Failure to achieve either of these will result in inefficient investment and management decisions, possibly with disastrous results - the decline of the Atlantic cod fishery is a classic example.

*Infrastructure Risk Management*

MWH such statistical models to develop infrastructure risk management (IRM), a decision support system and framework for Scottish Water for the management of every individual sewer and water pipe in Scotland. This involved using pipe-level statistical models to determine optimal investment requirements given specified levels of serviceability and budget.

The project was divided into four areas: data collection and processing; estimation of failure probabilities; quantification of the consequences of failure; and optimisation of benefits and costs. Data was a problem because many asset records were incomplete. Several statistically-based "imputation" techniques were used to overcome this - for example, statistical models were used to impute a missing age of a pipe based on other known attributes, such as the age of surrounding properties and the material type itself.

*Every pipe in Scotland*

Once we had an unbiased data set, failure models were built and tested to provide the expected failure rates of every pipe in Scotland, now and in the future. The expected failure rate of a pipe after intervention - for example, replacement, cleaning or relining - was also predicted and an associated cost assigned to each action.

The consequence of pipe failure was measured in both monetary and non-monetary terms (reactive costs, number of events, water quality, flooding, environmental, loss of service, customers affected, type of customer, reputation and so on). The key to calculating the consequence of failure is the direct link, spatial and temporal, between cause and effect.

For example, a key performance indicator for the water supply network is the number of customers who experience an unplanned outage. To calculate this, the network is traced to determine the number of customers that would be isolated if a pipe burst. These consequences were also judged against the "overall performance assessment" framework, which monitors the performance water companies provide to their customers.

*Cost/benefit analysis*

By benchmarking and quantifying the effect of an intervention, probability, cost, and consequence, against a do-nothing strategy, we determined the most cost beneficial strategy, under certain constraints. Of particular interest was the calculation of the minimal investment required to achieve yearly serviceability targets. For example, what is the investment needed to reduce bursts by 20 per cent over five years? Multiple constraints were also considered and resulted in considerable synergies between programmes.

Overall, IRM provided a defensible calculation of the sum of investment required to achieve fixed serviceability levels. At the same time, the method earmarked the specific pipe assets needing intervention during each year of the investment period and beyond. From the water company's point of view, the method provided confidence that the major sums of money being spent on capital maintenance were being spent in the best possible way.

Tim Watson is senior principal consultant with MWH Business Solutions.

For more information, visit the Water Statistics User Group