The negative binomial distribution as a model for external corrosion defect counts in buried pipelines

• Observed external-corrosion defects in underground pipelines revealed a tendency to cluster.
• The Poisson distribution is unable to fit extensive count data for these type of defects.
• In contrast, the negative binomial distribution provides a suitable count model for them.
• Two spatial stochastic processes lead to the negative binomial distribution for defect counts.
• They are the Gamma-Poisson mixed process and the compound Poisson process.
• A Rogeŕs process also arises as a plausible temporal stochastic process leading to corrosion defect clustering and to negative binomially distributed defect counts.

The spatial distribution of external corrosion defects in buried pipelines is usually described as a Poisson process, which leads to corrosion defects being randomly distributed along the pipeline. However, in real operating conditions, the spatial distribution of defects considerably departs from Poisson statistics due to the aggregation of defects in groups or clusters. In this work, the statistical analysis of real corrosion data from underground pipelines operating in southern Mexico leads to conclude that the negative binomial distribution provides a better description for defect counts. The origin of this distribution from several processes is discussed. The analysed processes are: mixed Gamma-Poisson, compound Poisson and Roger’s processes. The physical reasons behind them are discussed for the specific case of soil corrosion.