Using a Markov model to estimate pipe deterioration

The Markov process is a mathematical model used to recreate stochastic systems which have the property of being “memory-less”. That is; those systems for which the probability of being in any future state is dependent solely on the current state and not the past. These are often represented as two dimensional transition matrices indicating probability of going from one state to the next in one time period. Using a Markov process to model condition deterioration in pipes at first may seem counterintuitive. However there is some academic precedent for using Markov theory in pipe deterioration models (Kleiner et al. 2006).

Faced with limited known and traceable data on pipe condition in our networks, the Three Waters Asset Planning Team at Dunedin City Council (DCC) required a way to model deterioration for asset management purposes without any knowledge of condition history. A Markov process method was developed for estimating what was likely to happen based on what the current state was and how long the asset had to get to that state.

The method begins with breaking history into discrete periods. Assuming that a pipe is in condition 1 (excellent) when laid, all possible condition paths over those discrete time periods to the present day condition can be ascertained.

For example: if a pipe laid 4 time periods ago was now in condition 2 then there are 3 possible condition paths it may have taken: 1-1-1-2; 1-1-2-2; 1,2,2,2.

By taking a sample of pipes of the same material, laid at a similar time in history and assessing the individual conditions of all pipes in the sample, it is possible to estimate the probability of a given pipe being in a particular condition at the current time. Given that there are a finite number of paths to any one condition, the probability of each state to state transition in one time period can then be estimated.

Characteristic deterioration curves can be created based on weighting each path to the current condition by the probability of being in that condition at that point on the path. It has been these characteristic curves which have confirmed that this method captures known behaviour of certain pipe materials and therefore warrants further exploration.