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Markovian Analysis of Aging Distributed Systems Remaining Life

[+] Author Affiliations
Anna Bushinskaya

Science and Engineering Center “Reliability and Safety of Large Systems and Machines”, Yekaterinburg, RussiaUral State Agrarian University, Yekaterinburg, Russia

Sviatoslav Timashev

Science and Engineering Center “Reliability and Safety of Large Systems and Machines”, Yekaterinburg, RussiaUral State Agrarian University, Yekaterinburg, RussiaUral Federal University, Yekaterinburg, Russia

Paper No. IPC2014-33368, pp. V003T12A015; 7 pages
  • 2014 10th International Pipeline Conference
  • Volume 3: Materials and Joining; Risk and Reliability
  • Calgary, Alberta, Canada, September 29–October 3, 2014
  • Conference Sponsors: Pipeline Division
  • ISBN: 978-0-7918-4612-4
  • Copyright © 2014 by ASME


Correct assessment of the remaining life of distributed systems such as pipeline systems (PS) with defects plays a crucial role in solving the problem of their integrity.

Authors propose a methodology which allows estimating the random residual time (remaining life) of transition of a PS from its current state to a critical or limit state, based on available information on the sizes of the set of growing defects found during an in line inspection (ILI), followed by verification or direct assessment.

PS with many actively growing defects is a physical distributed system, which transits from one physical state to another. This transition finally leads to failure of its components, each component being a defect. Such process can be described by a Markov process.

The degradation of the PS (measured as monotonous deterioration of its failure pressure Pf (t)) is considered as a non-homogeneous pure death Markov process (NPDMP) of the continuous time and discrete states type. Failure pressure is calculated using one of the internationally recognized pipeline design codes: B13G, B31Gmod, DNV, Battelle and Shell-92.

The NPDMP is described by a system of non-homogeneous differential equations, which allows calculating the probability of defects failure pressure being in each of its possible states. On the basis of these probabilities the gamma-percent residual life of defects is calculated. In other words, the moment of time tγ is calculated, which is a random variable, when the failure pressure of pipeline defect Pf (tγ) > Pop, with probability γ, where Pop is the operating pressure. The developed methodology was successfully applied to a real life case, which is presented and discussed.

Copyright © 2014 by ASME



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