Abstract
In production processes, maintenance decisions are often made based on uncertain assessment of risk. This uncertainty may not only appear in the probability when a process component goes into a state of failure, but also in the cost of associated repairs, consequential damage, and opportunity cost of lost production. In this paper, repair of a component is modeled as a Markov process with multiple states under the assumption that with a sufficient number of states, the Markovian property is valid, that is, the transition probabilities from the current state describe the future state of the system. A Markov formulation is developed for a system component with states representing a range of operating, fault and repair situations. A risk function is calculated based on the sum of the products of cost estimate and transition probability for possible states.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Lipsett M (2001) Modeling the Flow of Information in Mine Maintenance Systems. Proc. CIM Annual Conference
Virtanen I (2006) On The Concepts And Derivation Of Reliability In Stochastic Systems With States Of Reduced Efficiency. Dissertation, University of Turku
Lugtigheid D, Banjevic D, Jardine A (2004) Modeling Repairable System Reliability with Explanatory Variables and Repair and Maintenance Actions. IMA J Manag Math 15:89-110. doi: 10.1093/imaman/15.2.89
Ching WK (2006) Markov chains: models, algorithms and applications. Springer, New York
Kececioglu D (1995) Maintainability, Availability and Operational Readiness Engineering Handbook. Prentice Hall, Upper Saddle River
Caldeira J, Taborda J, Trigo T (2006) Optimization of the preventive maintenance plan of a series components system. Int J Press Vessel Pip 83:244-248. doi: 10.1016/j.ijpvp.2006.02.016
Lindqvist B (2006) On the Statistical Modeling and Analysis of Repairable Systems. Statistical Science.Vol. 21, No.4, 532-551. doi: 10.1214/088342306000000448
Norris JR (1997) Markov Chains. Cambridge University Press, New York
Sahner R, Trivedi K (1986) A Hierarchical Combinatorial-Markov Method of Solving Complex Reliability Models. IEEE Computer Society Press, Los Alamitos CA. In Proceedings of FJCC. 1986, 817-825
Lisnianski A, Levitin G (2003) Multi-State System Reliability. World Scientific Publishing, Singapore.
D'Amico G, Janssen J, Manca R (2005) Credit Risk Migration Semi-Marko Models: A Reliability Approach
Zhang J (2005) Maintenance Planning and Cost Effective Replacement Strategies. Dissertation, University of Alberta
Modarres M, Kaminskiy M, Krivtsov V (1999) Reliability Engineering and Risk Analysis: A Practical Guide. Marcel Dekker, New York
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag London Limited
About this chapter
Cite this chapter
Lipsett, M.G., Gallardo Bobadilla, R. (2012). Modeling Risk in Discrete Multistate Repairable Systems. In: Amadi-Echendu, J., Willett, R., Brown, K., Mathew, J. (eds) Asset Condition, Information Systems and Decision Models. Engineering Asset Management Review. Springer, London. https://doi.org/10.1007/978-1-4471-2924-0_10
Download citation
DOI: https://doi.org/10.1007/978-1-4471-2924-0_10
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2923-3
Online ISBN: 978-1-4471-2924-0
eBook Packages: EngineeringEngineering (R0)