Stochastic Models in Preventive Maintenance Policies


Article Preview

In recent decades, philosophy behind maintenance has varied consistently due to the changes in complexity of designs, advances in automation and mechanization, adaptation to the fast growing market demand, commercial computation in the sectors, and environmental issues. In mid-forties, simplicity of designs, limited maintenance opportunities, and immaturity of trade culture made enough to perform only fix it when it broke approach, i.e. corrective maintenance, after failures. Last quarter of the 21th century made essential to constitute more conservative and preventive maintenance policies in order to ensure safety, reliability, and availability of systems with longer lifetime and cost effectiveness. Preventive maintenance can provide an economic saving more than 18% of operating cost of systems. In this basis, various stochastic models were proposed as a tool to constitute a maintenance policy to measure system availability and to obtain optimal maintenance periods. This paper presents a general perspective on common stochastic models in maintenance planning such as Homogenous Poisson Process, Non-Homogenous Poisson Process, and Imperfect Maintenance. The paper also introduces two common maintenance policies, block and age replacement policy, using these stochastic models.



Edited by:

Dashnor Hoxha, Francisco E. Rivera and Ian McAndrew




O. Gölbaşı and N. Demirel, "Stochastic Models in Preventive Maintenance Policies", Advanced Materials Research, Vol. 1016, pp. 802-806, 2014

Online since:

August 2014




* - Corresponding Author

[1] W. S. Wasson: System Analysis, Design, and Development: Concepts, Principles, and Practices (John Wiley and Sons, 2006).

[2] J. Moubray: Reliability-Centered Maintenance (Industrial Press Inc., 1997).

[3] A. Høyland and M. Rausand: System Reliability Theory: Models and Statistical Methods (John Wiley and Sons Inc., New Jersey 2004).

[4] S. Osaki: Stochastic System Reliability Modeling (World Scientific Publishing Co Pte Ltd., 1985).

[5] United States Department of Defense: Department of Defense Guide for Achieving Reliability, Availability, and Maintainability, (2005).

[6] J. L. Coetzee: The Role of NHPP Models in the Practical Analysis of Maintenance Failure Data. Reliability Engineering and System Safety, (1997), pp.161-168.


[7] Z. Chen: Bayesian and Empirical Bayes Approaches to Power Law Process and Microarray. Ph.D. Thesis (University of South Florida, 2004).

[8] T. Nakagawa, and K. Yasui: Optimum Policies for a System with Imperfect Maintenance. IEEE Transactions on Reliability, 36 (1987), pp.631-633.


[9] H. Pham and H. Wang: Imperfect Maintenance. European Journal of Operational Research , 94 (1996), pp.425-438.

[10] M. Kijima, H. Morimura, and Y. Suzuki: Periodical Replacement Problem Without Assuming the Minimal Repair. European Journal of Operational Research, 37 (1988), pp.194-203.


[11] T. Dohi, N. Kaio, and S. Osaki: Basic Preventive Maintenance Policies and Their Variations. In: M. Ben-Daya, S. O. Duffuaa, and A. Raouf, Maintenance, Modeling, and Optimization (Kluwer Academic Publishers, New York 2000).


[12] R. E. Barlow and F. Proschan: Mathematical Theory of Reliability (John Wiley and Sons Ltd., New York 1965).

[13] R. E. Barlow and L. C. Hunter: Optimum Preventive Maintenance Policies. Operations Research, 8 (1960), pp.90-100.