Abstract
A Multi-State System (MSS) is the type of mathematical model of a system in the reliability analysis in which both the system and its components may experience more than two reliability states. One of the possible approaches of MSS evaluation is based on system representation by a structure function that maps the system components states into the system state/reliability/availability (performance level). But the structure function can be used for completely specified data only. In this paper new method for structure function construction based on incomplete data is proposed. This method is based on the use of decision tree that is inducted according to initial data. A structure function is constructed as decision table that is formed by inducted decision tree.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Murchland, J.D.: Fundamental concepts and relations for reliability analysis of multistate system. In: Barlow, R.E., et al. (eds.) Reliability and Fault Tree Analysis: Theoretical and Applied Aspects of System Reliability, SIAM, Berkeley, pp. 581–618 (1975)
Natvig, B.: Multistate Systems Reliability Theory with Applications (2010)
Zaitseva, E., Levashenko, V.: Reliability analysis of multi-state system with application of multiple-valued logic. Int. J. Qual. Reliab. Manag. 34, 862–878 (2017)
Lisnianski, A., Frenkel, I., Karagrigoriou, A.: Recent Advances in Multi-State Systems Reliability. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-63423-4
Aven, T., Baraldi, P., Flage, R., Zio, E.: Uncertainty in Risk Assessment: The Representation and Treatment of Uncertainties by Probabilistic and Non-Probabilistic Methods (2014)
Maimon, O., Rokach, L.: Data Mining and Knowledge Discovery Handbook (2010)
Zaitseva, E., Levashenko, V.: Construction of a reliability structure function based on uncertain data. IEEE Trans. Reliab. 65, 1710–1723 (2016)
Miller, D.M., Drechsler, R.: On the construction of multiple-valued decision diagrams. In: Proceedings 32nd IEEE International Symposium on Multiple-Valued Logic, pp. 245–253 (2002)
Amari, S.V., Xing, L., Shrestha, A., Akers, J., Trivedi, K.S.: Performability analysis of multistate computing systems using multivalued decision diagrams. IEEE Trans. Comput. 59, 1419–1433 (2010)
Zaitseva, E., Levashenko, V.: Decision diagrams for reliability analysis of multi-state system. In: Proceedings of International Conference on Dependability of Computer Systems, DepCoS - RELCOMEX 2008, pp. 55–62 (2008)
Mo, Y.: A multiple-valued decision-diagram-based approach to solve dynamic fault trees. IEEE Trans. Reliab. 63, 81–93 (2014)
Zaitseva, E., Levashenko, V., Kostolny, J.: Multi-state system importance analysis based on direct partial logic derivative. In: Proceedings of 2012 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering, ICQR2MSE 2012, pp. 1514–1519 (2012)
Stankovic, R.S., Astola, J.T., Moraga, C.: Representations of Multiple-Valued Logic Functions. Morgan & Claypool Publishers, Princeton (2012)
Quinlan, J.R.: Induction of decision trees. Mach. Learn. 1, 81–106 (1986)
Quinlan, J.R.: C4.5: Programs for Machine Learning (Morgan Kaufmann Series in Machine Learning) (1992)
Levashenko, V., Zaitseva, E., Kvassay, M., Deserno, T.M.: Reliability estimation of healthcare systems using fuzzy decision trees. In: Proceedings of the 2016 Federated Conference on Computer Science and Information Systems, FedCSIS 2016 (2016)
Patel, H.R., Linares, A., Joseph, J.V.: Robotic and laparoscopic surgery: cost and training. Surg. Oncol. 18(3), 242–246 (2009)
Kvassay, M., Zaitseva, E., et al.: Minimal cut vectors and logical differential calculus. In: Proceedings of the International Symposium on Multiple-Valued Logic, pp. 167–172 (2014)
Kvassay, M., Zaitseva, E., Kostolny, J., Levashenko, V.: Importance analysis of multi-state systems based on integrated direct partial logic derivatives. In: Proceedings of the International Conference on Information and Digital Technologies (IDT 2015), pp. 183–195 (2015)
Acknowledgment
This work was partly supported by the grants of VEGA 1/0038/16, VEGA 1/0354/17 and APVV SK-FR-2017-003.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Forgac, A., Rabcan, J., Zaitseva, E., Lukyanchuk, I. (2019). Construction of the Structure Function of Multi-State System Based on Incompletely Specified Data. 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_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-91446-6_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91445-9
Online ISBN: 978-3-319-91446-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)