The approach proposed by Najjar and coworkers for the prediction of maximum pit depth is applied and validated through direct comparison with real pipeline steel pitting corrosion data. This methodology combines the Generalized Lambda Distribution (GLD) and the Bootstrap Method (BM) in order to estimate both the maximum pit depth and confidence intervals associated with the estimation. Samples are drawn from real-life pitting corrosion data and the GLD is used to obtain modeled pit depth distributions emulating the experimental ones. In order to estimate the maximum pit depth over an N -times larger area, simulated distributions, N -times larger than the experimental ones, are generated 10 4 times. The deepest pit depth is extracted from each simulated bootstrap sample to obtain a dataset of 10 4 extreme pit-depth values. An estimate of the maximum pit depth for the N -times larger surface can be obtained from this dataset by calculating the average of the 10 4 extreme values. The uncertainty in the estimation is derived from the 95% confidence interval of the bootstrap estimate. In this report, the results of the application of the GLD-BM framework are compared with extreme pit depth values observed in real pitting corrosion data. The agreement between the estimated and actual maximum pit depths points to the applicability of the GLD-BM as an alternative in estimating the maximum pit depth when only a small number of samples are available. The main advantage of the combined methodology over the Gumbel method is its great simplicity, since fast and reliable estimations can be made with at least only two experimental samples.

There exists a large number of works aimed at the application of Extreme Value Statistics to corrosion. However, there is a lack of studies devoted to the applicability of the Gumbel method to the prediction of maximum pitting-corrosion depth. This is especially true for works considering the typical pit densities and spatial patterns in long, underground pipelines. In the presence of spatial pit clustering, estimations could deteriorate, raising the need to increase the total inspection area in order to obtain the desired accuracy for the estimated maximum pit depth. In most practical situations, pit-depth samples collected along a pipeline belong to distinguishable groups, due to differences in corrosion environments. For example, it is quite probable that samples collected from the pipeline’s upper and lower external surfaces will differ and represent different pit populations. In that case, maximum pit-depth estimations should be made separately for these two quite different populations. Therefore, a good strategy to improve maximum pit-depth estimations is critically dependent upon a careful selection of the inspection area used for the extreme value analysis. The goal should be to obtain sampling sections that contain a pit population as homogenous as possible with regard to corrosion conditions. In this study, the aforementioned strategy is carefully tested by comparing extreme-value-oriented Monte Carlo simulations of maximum pit depth with the results of inline inspections. It was found that the variance to mean ratio, a measure of randomness, and the mean squared error of the maximum pit-depth estimations were considerably reduced, compared with the errors obtained for the entire pipeline area, when the inspection areas were selected based on corrosion-condition homogeneity.

Currently, the reliability of non-piggable pipelines is mainly assessed either from historical failure data or from the results of direct assessment evaluations. When external, localized corrosion is the main threat to the pipeline integrity, the most important factor in assessing the reliability of a pipeline segment is the distribution of maximum pit depths. This distribution cannot be directly derived from historical failure data, nor from the information obtained from external corrosion direct assessment. In contrast, the statistical modeling of extreme values could be used to predict the distribution of pit depth maxima in a pipeline from a relatively small number of maximum pit depths measured at excavation sites along its length. Despite of the large number of works aimed at the application of the extreme value statistics, there is a lack of studies devoted to the applicability of the method for prediction of the maximum pit depth for the pit densities and pit spatial patterns typical of long buried pipelines. In this work, Monte Carlo simulations were conducted in order to assess the statistical errors associated with the prediction of the maximum pit depth for a wide range of the number and size of the inspection areas, pits per unit area and pit spatial patterns. As a result, the optimum area of inspection is proposed. The Monte Carlo numerical experiments were run by using synthetic and real corrosion data acquired by magnetic flux leakage and ultrasonic in-line inspection (ILI) tools, an approach that has not been reported in previous studies. The ILI data was sampled using standard methods of extreme value analysis, and the predicted maximum pit depth was compared with that reported by the in-line inspection. Monte Carlo simulations with synthetic and real corrosion data have allowed assessing the influence of the number and size of the inspected areas on the accuracy of predictions when pits distribute homogeneously and non-homogeneously in the pipeline. It is shown that, when the distribution of pits is homogeneous, the accuracy in the maximum pit depth prediction using the proposed method is similar to the measurement errors associated with magnetic flux leakage ILI tools.

In this work, the statistical methods for the reliability of repairable systems have been used to produce a methodology capable to estimate the annualized failure rate of a pipeline population from the historical failure data of multiple pipelines systems. The proposed methodology provides point and interval estimators of the parameters of the failure intensity function for two of the most commonly applied stochastic models; the homogeneous Poisson process and the power law process. It also provides statistical tests to assess the adequacy of the stochastic model assumed for each system and to test whether all systems have the same model parameters. In this way, the failure data of multiple pipeline systems are only pooled to produce a generic failure intensity function when all systems follow the same stochastic model. This allows addressing both statistical and tolerance uncertainty adequately. The proposed methodology is outlined and illustrated using real life failure data of multiple oil and gas pipeline systems.