Abstract
Investigation of system reliability is a complex problem. Importance analysis of the system components is part of this investigation. Information about importance of the system components can also be used in system maintenance or in optimization of system reliability. In this paper we present how reliability function can be derived from the structure function of the system and how logic differential calculus allows us to investigate importance of the system components via time-dependent Birnbaum’s and criticality importance measures.
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References
Zio, E.: Reliability engineering: old problems and new challenges. Reliab. Eng. Syst. Saf. 94, 125–141 (2009)
Barlow, R.E., Proschan, F.: Statistical Theory of Reliability and Life Testing. Rinehart and Winston Holt, New York (1975)
Rausand, M., Høyland, A.: System Reliability Theory, 2nd edn. Wiley, Hoboken (2004)
Kaufmann, A., Grouchko, D., Cruon, R.: Mathematical Models for the Study of the Reliability of Systems. Academic Press, New York (1977)
Schneeweiss, W.G.: A short Boolean derivation of mean failure frequency for any (also non-coherent) system. Reliab. Eng. Syst. Saf. 94, 1363–1367 (2009)
Armstrong, M.J.: Reliability-importance and dual failure-mode components. IEEE Trans. Reliab. 46(2), 212–221 (1997)
Kvassay, M., Levashenko, V., Zaitseva, E.: Analysis of minimal cut and path sets based on direct partial Boolean derivatives. Proc. Inst. Mech. Eng. Part O: J. Risk Reliab. 230(2), 147–161 (2016)
Zaitseva, E., Levashenko, V., Kostolny, J.: Importance analysis based on logical differential calculus and Binary Decision Diagram. Reliab. Eng. Syst. Saf. 138, 135–144 (2015)
Kuo, W., Zhu, X.: Importance Measures in Reliability, Risk, and Optimization: Principles and Applications. Wiley, Hoboken (2012)
Steinbach, B., Posthoff, C.: Boolean Differential Calculus. In: Synthesis Lectures on Digital Circuits and Systems, vol. 12, no. 1, pp. 1–215 (2017)
Powell, G.: Beginning Database Design. Wiley, Hoboken (2006)
Klein, A.: Backblaze hard drive stats for 2016 (2016). https://www.backblaze.com/blog/hard-drive-benchmark-stats-2016/. Accessed 20 Dec 2017
Elerath, J.G.: AFR: Problems of definition, calculation and measurement in a commercial environment. In: Annual Reliability and Maintainability Symposium, pp. 71–76 (2000)
Szabados, D.: Diving into ‘MTBF’ and ‘AFR’: Storage reliability specs explained. https://web.archive.org/web/20100501151901/, http://enterprise.media.seagate.com/2010/04/inside-it-storage/diving-into-mtbf-and-afr-storage-reliability-specs-explained/. Accessed 20 Dec 2017
Burgess, M.: Analytical Network and System Administration: Managing Human-Computer Systems. Wiley, Hoboken (2012)
Acknowledgment
This work was partly supported by the grants VEGA 1/0038/16 and 1/0354/17.
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Rusnak, P., Rabcan, J., Kvassay, M., Levashenko, V. (2019). Time-Dependent Reliability Analysis Based on Structure Function and Logic Differential Calculus. In: Zamojski, W., Mazurkiewicz, J., Sugier, J., Walkowiak, T., Kacprzyk, J. (eds) Contemporary Complex Systems and Their Dependability. DepCoS-RELCOMEX 2018. Advances in Intelligent Systems and Computing, vol 761. Springer, Cham. https://doi.org/10.1007/978-3-319-91446-6_38
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DOI: https://doi.org/10.1007/978-3-319-91446-6_38
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