Markov chain models for modelling pipeline deterioration

Abstract

A Markov Chain is a model of a sequence of event transitions in which the transitions from one event to other events occur with a fixed probability for a fixed time duration. In general both the events and time steps are taken to be discrete variables. These properties of Markov chains have led them to be used for modelling deterioration processes. Pipeline deterioration is an important infrastructure issue, since most cities worldwide face the problems of managing aging infrastructure. A deterioration model is required in order to plan maintenance budgets effectively, rather than engaging in ad-hoc repairs. While periodic inspections would provide a rich data set for constructing the Markov model, often most public utility agencies can only manage a set of ‘snapshot’ data, where the conditions of pipes (of different ages) have been ascertained at a single point in time, since pipeline inspection is difficult to carry out during service.

In this work, we obtain a snapshot dataset of pipeline conditions from the literature. We demonstrate that simple time series modelling is not effective for capturing such deterioration. The Markov chain is defined by an upper triangular matrix - of size 4x4 if we assume 4 discrete states of deterioration as done by the previous authors. Although they have used a Monte Carlo method to obtain the elements of the matrix, we demonstrate that a Genetic Algorithm approach will give similar results. We also demonstrate the variation in level of service of two different maintenance strategies (i.e. the maintenance of pipes at various percentages of different states), where only complete replacement is carried out, but at different time intervals.