Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-11T10:16:03.309Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-Dimensional Signatures

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  04 February 2016

Ilya Gertsbakh ,
Yoseph Shpungin  and
Fabio Spizzichino
Ilya Gertsbakh*
Affiliation:
Ben Gurion University
Yoseph Shpungin*
Affiliation:
Shamoon College of Engineering
Fabio Spizzichino*
Affiliation:
Sapienza University of Rome
*
∗ Postal address: Department of Mathematics, Ben Gurion University, Shai Agnon 30/25, 69362, Tel-Aviv, Israel. Email address: [email protected]
∗∗ Postal address: Deptartment of Software Engineering, Shamoon College of Engineering, Bialik/Basel Streets, Beer Sheva, Israel. Email address: [email protected]
∗∗∗ Postal address: Deptartment of Mathematics, Sapienza University of Rome, Piazzale Aldo Moro 2, 00185, Rome, Italy. Email address: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The notion of the signature is a basic concept and a powerful tool in the analysis of networks and reliability systems of binary type. An appropriate definition of this concept has recently been introduced for systems that have ν possible states (with ν ≥ 3). In this paper we analyze in detail several properties and the most relevant aspects of such a general definition. For simplicity's sake, we focus our attention on the case ν = 3. Our analysis will however provide a number of hints for understanding the basic aspects of the general case.

Keywords

Two-dimensional anchortwo-dimensional signatureG-series and G-parallel systemsmultistate recurrent systemhomogeneous polynomial

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 416 - 429
Copyright
© Applied Probability Trust 

References

Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
Boland, P. J. (2001). Signatures of indirect majority systems. J. Appl. Prob. 38, 597–603.Google Scholar
Boland, P. J., Samaniego, F. J. and Vestrup, E. M. (2003). Linking dominations and signatures in network reliability theory. In Mathematical and Statistical Methods in Reliability (Trondheim, 2002), World Scientific, River Edge, NJ, pp. 89–103.Google Scholar
Da, G., Zheng, B. and Hu, T. (2012). On computing signatures of coherent systems. J. Multivariate Anal. 103, 142–150.Google Scholar
Elperin, T., Gertsbakh, I. and Lomonosov, M. (1991). Estimation of network reliability using graph evolution models. IEEE Trans. Reliab. 40, 572–581.Google Scholar
Gertsbakh, I. and Shpungin, Y. (2004). Combinatorial approaches to Monte Carlo estimation of network lifetime distribution. Appl. Stoch. Models Business Industry 20, 49–57.CrossRefGoogle Scholar
Gertsbakh, I. B. and Shpungin, Y. (2009). Models of Network Reliability: Analysis, Combinatorics, and Monte Carlo. CRC Press, Boca Raton, FL.Google Scholar
Gertsbakh, I. and Shpungin, Y. (2011). Network Reliability and Resilience. Springer.Google Scholar
Gertsbakh, I. and Shpungin, Y. (2012). Multidimensional spectra of multistate systems with binary components. In Recent Advances in System Reliability, eds Lisniansky, A. and Frenkel, I., Springer, London, pp. 49–61.Google Scholar
Gertsbakh, I., Shpungin, Y. and Spizzichino, F. (2011). Signatures of coherent systems built with separate modules. J. Appl. Prob. 48, 843–855.CrossRefGoogle Scholar
Kochar, S., Mukerjee, H. and Samaniego, F. J. (1999). The “signature” of a coherent system and its application to comparisons among systems. Naval Res. Logistics 46, 507–523.Google Scholar
Levitin, G., Gertsbakh, I. and Shpungin, Y. (2011). Evaluating the damage associated with intentional network disintegration. Reliab. Eng. System Safety 96, 433–439.Google Scholar
Lisnianski, A. and Levitin, G. (2003). Multi-State System Reliability. World Scientific, River Edge, NJ.CrossRefGoogle Scholar
Navarro, J., Samaniego, F. J. and Balakrishnan, N. (2010). The Joint signature of coherent systems with shared components. J. Appl. Prob. 47, 235–253.Google Scholar
Navarro, J., Samaniego, F. J., Balakrishnan, N. and Bhattacharaya, D. (2008). On the application and extension of system signatures in engineering reliability. Naval Res. Logistics 55, 314–326.Google Scholar
Samaniego, F. J. (1985). On the closure of the IFR class under formation of coherent systems. IEEE Trans. Reliab. R-34, 69–72.Google Scholar
Samaniego, F. J. (2007). System Signatures and Their Application in Engineering Reliability. Springer, New York.Google Scholar
Spizzichino, F. (2008). The role of signature and symmetrization for systems with non-exchangeable components. In Advances in Mathematical Modeling for Reliability, eds Bedford, T. \et, IOS Press, Amsterdam, pp. 138–148.Google Scholar
Spizzichino, F. and Navarro, J. (2012). Signatures and symmetry properties of coherent systems. In Recent Advances in System Reliability, eds Lisniansky, A. and Frenkel, I., Springer, London, pp. 33–48.Google Scholar