Reliable Inference for the Maximum Pit Depth within Pitting Colonies on Long Pipelines

This paper proposes a model for statistical dependence between pit depths when monitoring a pipeline for corrosion. The model is flexible in terms of the shape and endpoint behavior of the distribution of the pit depths, and in terms of the degree of dependence between observations. Illustrative examples are provided for several choices of model parameters. Explicit confidence bounds for the maximum pit depth are derived; a sequential sampling plan for obtaining sufficiently precise estimates is proposed; and procedures for testing whether the maximum pit depth is above or below a certain threshold are given.