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Mathematical Problems in Engineering
Volume 2013, Article ID 108386, 13 pages
Research Article

Markov Chain Models for the Stochastic Modeling of Pitting Corrosion

1Departamento de Ingeniería Metalúrgica, IPN-ESIQIE, UPALM s/n, Edificio 7, Zacatenco, 07738 México, DF, Mexico
2Universidad Autónoma de la Ciudad de México, 09790 México, DF, Mexico
3Departamento de Ingeniería Química Industrial, ESIQIE-IPN, UPALM Edificio 7, Zacatenco, 07738 México, DF, Mexico

Received 1 February 2013; Revised 19 April 2013; Accepted 3 May 2013

Academic Editor: Wuquan Li

Copyright © 2013 A. Valor et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth) Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.