Abstract
Nowadays, the data storage system is an integral part of our lives. Therefore, the main focus is in making this system reliable and accessible at all times. Reliability analysis of such systems provides insight into the components and topological parts of the system, in which a system is most vulnerable. Several approaches can be chosen to represent the system, one of the most used is known as the structure function. This approach allows us to represent a system of any complexity and also allows us to use the tools of logic algebra such as logic differential calculus. The aim of this work is to show the use of logic differential calculus and structure function for the calculation of the time-dependent importance measures for components in the time-dependent reliability analysis of the selected data storage system. After the computation of all importance measures, the problem areas of the data storage will be identified from a reliability point of view.
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References
Zio, E.: Reliability engineering: old problems and new challenges. Reliab. Eng. Syst. Saf. 94, 125–141 (2009). doi:https://doi.org/10.1016/J.RESS.2008.06.002
Block, H.W., Barlow, R.E., Proshan, F.: Statistical theory of reliability and life testing: probability models. J. Am. Stat. Assoc. 72, 227 (1977). doi:https://doi.org/10.2307/2286944
Rausand, M., Høyland, A.: System Reliability Theory: Models, Statistical Methods, and Applications. Wiley (2003)
Grouchko, D., Kaufmann, A., Cruon, R.: Mathematical Models for the Study of the Reliability of Systems, Elsevier Science (1977)
Natvig, B., Multistate Systems Reliability Theory with Applications, Wiley (2010)
Lisnianski, A., Levitin, G.: Multi-State System Reliability: Assessment, Optimization and Applications, World Scientific (2003)
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). doi:https://doi.org/10.1016/j.ress.2008.12.001
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, 147–161 (2016). doi:https://doi.org/10.1177/1748006X15598722
Armstrong, M.J.: Reliability-importance and dual failure-mode components. IEEE Trans. Reliab. 46, 212–221 (1997). doi:https://doi.org/10.1109/24.589949
Zhang, J.: Multi-function system reliability. In: Proceedings – Annual Reliability and Maintainability Symposium. Institute of Electrical and Electronics Engineers Inc (2019)
Marichal, J.L.: Structure functions and minimal path sets. IEEE Trans. Reliab. 65, 763–768 (2016). doi:https://doi.org/10.1109/TR.2015.2513017
Brinzei, N., Aubry, J.-F.: Graphs models and algorithms for reliability assessment of coherent and non-coherent systems. Proc. Inst. Mech. Eng. Part O J. Risk Reliab. 232, 201–215. doi:https://doi.org/10.1177/1748006X17744381
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). doi:https://doi.org/10.1016/J.RESS.2015.01.009
Kuo, W., Zhu, X.: Importance Measures in Reliability, Risk, and Optimization: Principles and Applications, John Wiley and Sons (2012)
Silberschatz, A., Galvin, P.B., Gagne, G.: Operating System Concepts, 10th edn. John Wiley & Sons, Inc. (2018)
Butler, D.: (1979) Complete importance ranking for components of binary coherent systems, with extensions to multi-state systems. Nav. Res. Logist. Q. doi:https://doi.org/10.1002/nav.3800260402
Al Luhayb, A.S.M., Coolen-Maturi, T., Coolen, F.P.A.: Smoothed bootstrap for survival function inference. In: Proceedings of the International Conference on Information and Digital Technologies 2019, IDT 2019. Institute of Electrical and Electronics Engineers Inc., pp. 296–303 (2019)
Papadopoulos, V., Giovanis, D.G.: Reliability analysis. In: Mathematical Engineering, pp. 71–98. Springer Verlag (2018)
Steinbach, B., Posthoff, C.: Boolean differential calculus. Synth. Lect. Digit. Circuits Syst. 12, 1–217 (2017). doi:https://doi.org/10.2200/S00766ED1V01Y201704DCS052
Yanushkevich, S.N., Michael Miller, D., Shmerko, V.P., Stanković, R.S.: Decision Diagram Techniques for Micro- and Nanoelectronic Design: Handbook, CRC Press (2005)
Rusnak, P., Rabcan, J., Kvassay, M., Levashenko, V.: Time-dependent reliability analysis based on structure function and logic differential calculus. In: Advances in Intelligent Systems and Computing, pp. 409–419 (2019)
Klein, A.: Backblaze Hard Drive Stats for 2019 https://www.backblaze.com/blog/hard-drive-stats-for-2019/ (2020). Accessed 11 Oct 2020
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This work was supported by the Slovak Research and Development Agency under the grant No. SK-SRB-18-0002.
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Rusnak, P., Mrena, M. (2021). Time Dependent Reliability Analysis of the Data Storage System Based on the Structure Function and Logic Differential Calculus. In: van Gulijk, C., Zaitseva, E. (eds) Reliability Engineering and Computational Intelligence. Studies in Computational Intelligence, vol 976. Springer, Cham. https://doi.org/10.1007/978-3-030-74556-1_11
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DOI: https://doi.org/10.1007/978-3-030-74556-1_11
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