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Exact reliability quantification of highly reliable systems with maintenance

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  • BriÅ¡, Radim

Abstract

When a system is composed of highly reliable elements, exact reliability quantification may be problematic, because computer accuracy is limited. Inaccuracy can be due to different aspects. For example, an error may be made when subtracting two numbers that are very close to each other, or at the process of summation of many very different numbers, etc. The basic objective of this paper is to find a procedure, which eliminates errors made by PC when calculations close to an error limit are executed. Highly reliable system is represented by the use of directed acyclic graph which is composed from terminal nodes, i.e. highly reliable input elements, internal nodes representing subsystems and edges that bind all of these nodes. Three admissible unavailability models of terminal nodes are introduced, including both corrective and preventive maintenance. The algorithm for exact unavailability calculation of terminal nodes is based on merits of a high-performance language for technical computing MATLAB. System unavailability quantification procedure applied to a graph structure, which considers both independent and dependent (i.e. repeatedly occurring) terminal nodes is based on combinatorial principle. This principle requires summation of a lot of very different non-negative numbers, which may be a source of an inaccuracy. That is why another algorithm for exact summation of such numbers is designed in the paper. The summation procedure uses benefits from a special number system with the base represented by the value 232. Computational efficiency of the new computing methodology is compared with advanced simulation software. Various calculations on systems from references are performed to emphasize merits of the methodology.

Suggested Citation

  • BriÅ¡, Radim, 2010. "Exact reliability quantification of highly reliable systems with maintenance," Reliability Engineering and System Safety, Elsevier, vol. 95(12), pages 1286-1292.
    • Handle: RePEc:eee:reensy:v:95:y:2010:i:12:p:1286-1292
    DOI: 10.1016/j.ress.2010.06.004
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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. Choi, Jong Soo & Cho, Nam Zin, 2007. "A practical method for accurate quantification of large fault trees," Reliability Engineering and System Safety, Elsevier, vol. 92(7), pages 971-982.
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    1. Radim Briš & Pavel Jahoda, 2022. "Really Ageing Systems Undergoing a Discrete Maintenance Optimization," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    2. Bris, Radim & Medonos, Sava & Wilkins, Chris & Zdráhala, Adam, 2014. "Time-dependent risk modeling of accidental events and responses in process industries," Reliability Engineering and System Safety, Elsevier, vol. 125(C), pages 54-66.
    3. Briš, Radim & Byczanski, Petr, 2013. "Effective computing algorithm for maintenance optimization of highly reliable systems," Reliability Engineering and System Safety, Elsevier, vol. 109(C), pages 77-85.
    4. Radim Briš & 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.

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