Two-dimensional signatures
Ilya Gertsbakh, Yoseph Shpungin, and Fabio Spizzichino
Source: J. Appl. Probab. Volume 49, Number 2
(2012), 416-429.
Abstract
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.
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Keywords: Two-dimensional anchor; two-dimensional signature; G-series and G-parallel systems; multistate recurrent system; homogeneous polynomial
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Permanent link to this document: http://projecteuclid.org/euclid.jap/1339878795
Digital Object Identifier: doi:10.1239/jap/1339878795
Zentralblatt MATH identifier: 06053720
Mathematical Reviews number (MathSciNet): MR2977804
References
Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.
Mathematical Reviews (MathSciNet): MR438625
Zentralblatt MATH: 0379.62080
Boland, P. J. (2001). Signatures of indirect majority systems. J. Appl. Prob. 38, 597–603.
Mathematical Reviews (MathSciNet): MR1834763
Zentralblatt MATH: 1042.62090
Digital Object Identifier: doi:10.1239/jap/996986765
Project Euclid: euclid.jap/996986765
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.
Mathematical Reviews (MathSciNet): MR2031068
Digital Object Identifier: doi:10.1142/9789812795250_0007
Da, G., Zheng, B. and Hu, T. (2012). On computing signatures of coherent systems. J. Multivariate Anal. 103, 142–150.
Mathematical Reviews (MathSciNet): MR2823715
Zentralblatt MATH: 05963982
Digital Object Identifier: doi:10.1016/j.jmva.2011.06.015
Elperin, T., Gertsbakh, I. and Lomonosov, M. (1991). Estimation of network reliability using graph evolution models. IEEE Trans. Reliab. 40, 572–581.
Gertsbakh, I. and Shpungin, Y. (2004). Combinatorial approaches to Monte Carlo estimation of network lifetime distribution. Appl. Stoch. Models Business Industry 20, 49–57.
Mathematical Reviews (MathSciNet): MR2109350
Digital Object Identifier: doi:10.1002/asmb.514
Gertsbakh, I. B. and Shpungin, Y. (2009). Models of Network Reliability: Analysis, Combinatorics, and Monte Carlo. CRC Press, Boca Raton, FL.
Mathematical Reviews (MathSciNet): MR2583184
Gertsbakh, I. and Shpungin, Y. (2011). Network Reliability and Resilience. Springer.
Gertsbakh, I. and Shpungin, Y. (2012). Multidimensional spectra of multistate systems with binary components. In Recent Advances in System Reliability, eds A. Lisniansky and I. Frenkel, Springer, London, pp. 49–61.
Mathematical Reviews (MathSciNet): MR2905497
Digital Object Identifier: doi:10.1007/978-1-4471-2207-4_4
Gertsbakh, I., Shpungin, Y. and Spizzichino, F. (2011). Signatures of coherent systems built with separate modules. J. Appl. Prob. 48, 843–855.
Mathematical Reviews (MathSciNet): MR2884820
Digital Object Identifier: doi:10.1239/jap/1316796919
Project Euclid: euclid.jap/1316796919
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.
Mathematical Reviews (MathSciNet): MR1700160
Digital Object Identifier: doi:10.1002/(SICI)1520-6750(199908)46:5<507::AID-NAV4>3.0.CO;2-D
Levitin, G., Gertsbakh, I. and Shpungin, Y. (2011). Evaluating the damage associated with intentional network disintegration. Reliab. Eng. System Safety 96, 433–439.
Lisnianski, A. and Levitin, G. (2003). Multi-State System Reliability. World Scientific, River Edge, NJ.
Mathematical Reviews (MathSciNet): MR1980576
Navarro, J., Samaniego, F. J. and Balakrishnan, N. (2010). The joint signature of coherent systems with shared components. J. Appl. Prob. 47, 235–253.
Mathematical Reviews (MathSciNet): MR2654770
Digital Object Identifier: doi:10.1239/jap/1269610828
Project Euclid: euclid.jap/1269610828
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.
Mathematical Reviews (MathSciNet): MR2402184
Digital Object Identifier: doi:10.1002/nav.20285
Samaniego, F. J. (1985). On the closure of the IFR class under formation of coherent systems. IEEE Trans. Reliab. R-34, 69–72.
Samaniego, F. J. (2007). System Signatures and Their Application in Engineering Reliability. Springer, New York.
Mathematical Reviews (MathSciNet): MR2380178
Spizzichino, F. (2008). The role of signature and symmetrization for systems with non-exchangeable components. In Advances in Mathematical Modeling for Reliability, eds T. Bedford \et, IOS Press, Amsterdam, pp. 138–148.
Mathematical Reviews (MathSciNet): MR2464240
Spizzichino, F. and Navarro, J. (2012). Signatures and symmetry properties of coherent systems. In Recent Advances in System Reliability, eds A. Lisniansky and I. Frenkel, Springer, London, pp. 33–48.
Mathematical Reviews (MathSciNet): MR2905496
Digital Object Identifier: doi:10.1007/978-1-4471-2207-4_3
Journal of Applied Probability
