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

• Published in: Corrosion (Houston, Tex.) Tex.), 2003-12, Vol.59 (12), p.1058-1063
• Main Author: Martinsek, A.T.
• Format: Article
• Language: English
• Subjects: Applied sciences; Colonies; Confidence; Corrosion; Corrosion environments; Dependence; Depth; Exact sciences and technology; Mathematical models; Metals. Metallurgy; Sequential sampling; Submarine pipelines
• ISSN: 0010-9312; 1938-159X
• DOI: 10.5006/1.3277525

ABSTRACTIn his 1996 W.R. Whitney Award Lecture, Shibata1 noted that the statistical models most commonly used in applications to pitting corrosion assume independence, even though "it is likely that pitting events are not independent but are mutually dependent." Although a great deal of excellent work in corrosion engineering has been done using methods based on independent data, it is clearly desirable to develop tractable models and methods of inference that appropriately reflect the dependence that is inherent in pitting corrosion. The present paper describes one such model that may be appropriate in certain situations. The model is a relatively simple one, and it is flexible in terms of both distributional shape and degree of dependence between observations. Moreover, statistical analysis based on the model is straightforward given recent theoretical developments. Consider the following situation. One is monitoring a pipeline for corrosion by sending a remotecontrolled sensor through the pipeline. As it moves, the sensor takes ultrasound readings of pit depth. At each location the sensor records the largest pit depth in that cross section of the pipe. We will assume that the locations are equally spaced. The recorded pit depths are clearly bounded, for there are maximum and minimum pit depths in the pipeline. Because we are only sampling the pit depths rather than observing all pit depths in the pipeline, the maximum and minimum are unknown. The goal is to estimate the maximum pit depth, so that a decision can be made on whether or not to replace the pipeline.DESCRIPTION AND PROPERTIES OF THE MODELThe sampled pit depths will be denoted by X1, X2, X3, ..., corresponding to the first, second, third, etc., locations at which the readings are taken; the maximum and minimum pit depths in the pipeline will be denoted by b and a, respectively. We will assume that all of the random variables Xi have the same marginal probability distribution, and that this distribution is beta on the interval [a,b], with unknown parameters and , that is: