JAMP  Vol.8 No.4 , April 2020
Probabilistic Model of Cumulative Damage in Pipelines Using Markov Chains
Abstract: This paper presents a probabilistic model of cumulative damage based on Markov chains theory to model propagation of internal corrosion depth localized in a hydrocarbons transport pipeline. The damage accumulation mechanism is unit jump type, depending on the state. It uses a shock model based on Bernoulli trials and probabilities to remain in the same state or the next one. Data are adjusted to Lognormal distribution and proven with a Kolmogórov-Smirnov test. The vector obtained from multiplying the initial state vector with the transition matrix was developed and the system of equations to find each transition probability with a single inspection report was solved. In order to calculate propagation of internal corrosion after inspection, an exponential equation was proposed and a parameter was adjusted to the data. Time to expected failure was obtained by adding the time expected in each damage state. Each time step was adjusted to real time.
Cite this paper: Casanova-del-Angel, F. , Flores-Méndez, E. and Cortes-Yah, K. (2020) Probabilistic Model of Cumulative Damage in Pipelines Using Markov Chains. Journal of Applied Mathematics and Physics, 8, 620-642. doi: 10.4236/jamp.2020.84048.

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