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On innovative stochastic renewal process models for exact unavailability quantification of highly reliable systems

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  • Radim BriÅ¡
  • Petr Byczanski

Abstract

In previous research, we developed original methodology for high-performance computing which enables exact unavailability quantification of a real maintained highly reliable system containing highly reliable components with both preventive and corrective maintenance. Whereas the original methodology was developed for systems containing components with exponential lifetime distribution, the main objective of this article is generalization of the methodology by applying stochastic alternating renewal process models, so as to be used for unavailability quantification of systems containing arbitrary components without any restrictions on the form of the probability distribution assigned to time to failure and repair duration, that is, aging components will be allowed. For this purpose, a recurrent linear integral equation for point unavailability is derived and proved. This innovative equation is particularly eligible for numerical implementation because it does not contain any renewal density, that is, it is more effective for unavailability calculation than the corresponding equation resulting from the traditional alternating renewal process theory, which contains renewal density. The new equation undergoes the process of discretization which results in numeric formula to quantify desired unavailability function. The numerical process is elaborated for all previously intended stochastic component models. Found component unavailability functions are used to quantify unavailability of a complex maintained system. System is represented by the use of directed acyclic graph, which proved to be very effective system representation to quantify reliability of highly reliable systems.

Suggested Citation

  • Radim BriÅ¡ & Petr Byczanski, 2017. "On innovative stochastic renewal process models for exact unavailability quantification of highly reliable systems," Journal of Risk and Reliability, , vol. 231(6), pages 617-627, December.
    • Handle: RePEc:sae:risrel:v:231:y:2017:i:6:p:617-627
    DOI: 10.1177/1748006X17717617
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    References listed on IDEAS

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    1. Briš, Radim, 2008. "Parallel simulation algorithm for maintenance optimization based on directed Acyclic Graph," Reliability Engineering and System Safety, Elsevier, vol. 93(6), pages 874-884.
    2. Myers, Albert F. & Rauzy, Antoine, 2008. "Assessment of redundant systems with imperfect coverage by means of binary decision diagrams," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 1025-1035.
    3. van der Weide, J.A.M. & Pandey, Mahesh D., 2015. "A stochastic alternating renewal process model for unavailability analysis of standby safety equipment," Reliability Engineering and System Safety, Elsevier, vol. 139(C), pages 97-104.
    4. Briš, Radim, 2010. "Exact reliability quantification of highly reliable systems with maintenance," Reliability Engineering and System Safety, Elsevier, vol. 95(12), pages 1286-1292.
    5. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, February.
    6. Simon, C. & Weber, P. & Evsukoff, A., 2008. "Bayesian networks inference algorithm to implement Dempster Shafer theory in reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 950-963.
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