Markov approach to early diagnostics, reliability assessment, residual life and optimal maintenance of pipeline systems

In this paper the pipeline degradation – simultaneous growth of many corrosion defects and reduction of pipe residual strength (burst pressure) is described by Markov processes of pure birth and pure death type, respectively. This allows considering collective (joint) behavior of the set of actively growing defects in the pipeline as a distributed system, and to eliminate restrictions of the classical approach. On the basis of constructed Markov models following methods are proposed: (1) a method for assessing the probability of failure (POF)/reliability of a single defective pipeline cross-section and of a pipeline as a distributed system; (2) a practical assessment of the gamma-percent residual life of pipeline systems (PS); (3) an adequate economic model for assessing the optimum time for performing the next inline inspection (ILI) or PS maintenance/repair, which minimizes maintenance expenditures; (4) method of estimating the information entropy generated by degradation of the defective pipeline cross-section. This permits establishing relations between different physical and probabilistic states of the PS and opens new possibilities for its early diagnostics and optimizing its maintenance.