Analysis of Boundary States of Multi-state System by Direct Partial Logic Derivatives
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Multi-State System (MSS) is mathematical model that is used in reliability engineering for the representation of initial investigated object (system). In a MSS, both the system and its components may experience more than two states (performance levels). One of possible description of MSS is a structure function that is defined correlation between a system components states and system performance level. The investigation of a structure function allows obtaining different properties, measures and indices for MSS reliability. For example, boundary system’s states, probabilities of a system performance levels and other measures are calculated based a structure function. In this paper mathematical approach of Direct Partial Logical Derivatives is proposed for calculation of boundary states of MSS.
KeywordsMulti-state system Multiple-valued logic Direct partial logic derivatives Boundary state
This work was partially supported by grant of Scientific Grant Agency of the Ministry of Education of Slovak Republic (Vega 1/0498/14).
- 2.Praks, P., Kopustinskas, V.: Monte-carlo based reliability modelling of a gas network using graph theory approach. In: 2014 Ninth International Conference on Availability, Reliability and Security, pp. 380–386. IEEE (2014)Google Scholar
- 3.Zaitseva, E., Levashenko, V., Rusin, M.: Reliability analysis of healthcare system. In: FedCSIS 2011 Federated Conference on Computer Science and Information Systems, pp. 169–175. IEEE (2011)Google Scholar
- 5.Murchland, J.D.: Fundamental concepts and relations for reliability analysis of multistate system. In: Reliability and Fault Tree Analysis, Theoretical and Applied Aspects of System Reliability, SIAM, pp. 581–618 (1975)Google Scholar
- 9.Xie, M., Dai, Y.-S., Poh, K.-L.: Multi-state system reliability. In: Computing System Reliability Models and Analysis, pp. 207–237. Kluwer Academic Publishers, New York (2004)Google Scholar
- 14.Reinske, K., Ushakov, I.: Application of graph theory for reliability analysis. Radio i Sviaz, Moscow, USSR (1988) (in Russian)Google Scholar
- 18.Kvassay, M., Zaitseva, E., Levashenko, V.: Minimal cut sets and direct partial logic derivatives in reliability analysis. In: Proceedings of the European Safety and Reliability Conference on Safety and Reliability: Methodology and Applications, pp. 241–248. CRC Press (2014)Google Scholar
- 19.Miller, M.D., Thornton, M.A.: Multiple Valued Logic: Concepts and Representations. Synthesis Lectures on Digital Circuits and systems. Morgan and Claypool Publishers, San Rafael (2008)Google Scholar
- 20.Zaitseva, E., Kovalik, S., Levashenko, V., Matiaško, K.: Algorithm for dynamic analysis of multi-state system by structure function. In: IEEE International Conference on Computer as a Tool, pp.1224–1227. IEEE Press (2005)Google Scholar
- 21.Zaitseva, E.: Dynamic reliability indices for multi-state system. In: The 33th IEEE International Symposium on Multiple-Valued Logic, pp. 287–292. IEEE Press (2003)Google Scholar
- 25.Kapur, K.C., Zaitseva, E., Kovalik, S., Matiasko, K.: Customer-driven reliability models and logical differential calculus for reliability analysis of multi state system. J. KONBIN 1, 39–47 (2006)Google Scholar
- 26.Zaitseva, E., Levashenko, V., Kostolny, J., Kvassay, M.: Direct partial logic derivatives in analysis of boundary states of multi-state system. In: 11th International Conference on ICT in Education, Research and Industrial Applications: Integration, Harmonization and Knowledge Transfer, pp. 535–549. CEUR-WS (2015)Google Scholar