Signatures and symmetry properties of coherent systems

Springer Series in Reliability Engineering

Volumn 51, Issue , 2012, Pages 33-48

  Spizzichino, Fabio ^a   Navarro, Jorge ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF MURCIA   (Spain)

Author keywords

Average systems; Order statistics exchangeability; Projected systems; Signature exchangeability; Weak exchangeability; Well designed systems

Indexed keywords

INDUSTRIAL ENGINEERING;

AVERAGE SYSTEM; ORDER STATISTICS; PROJECTED SYSTEMS; SIGNATURE-EXCHANGEABILITY; WEAK-EXCHANGEABILITY;

ENGINEERING;

EID: 84952012943     PISSN: 16147839     EISSN: 2196999X     Source Type: Book Series    
DOI: 10.1007/978-1-4471-2207-4_3     Document Type: Chapter

References (23)

1. Barlow RE, Proschan F (1975) Statistical theory of reliability and life testing: probability models. Holt, Rinehart and Wiston, New York
2. Block HW, Dugas MR, Samaniego FJ (2007a) Characterizations of the relative behavior of two systems via properties of their signature vectors. In: Balakrishnan N, Sarabia JM, Castillo E (eds) Advances in distribution theory, order statistics and inference. Birkhäuser, Boston, pp 279–289
3. Block HW, Dugas MR, Samaniego FJ (2007b) Signature-related results on system lifetimes. In: Nair V (ed) Advances in statistical modeling and inference. World Scientific, Singapore, pp 115–129
4. Boland PJ (2001) Signature of indirect majority systems. J Appl Probab 38(2):597–603
5. Boland PJ, Samaniego FJ (2004a) Stochastic ordering results for consecutive k-out-of-n systems. IEEE Trans Reliab 53(1):7–10
6. Boland PJ, Samaniego FJ (2004b) The signature of a coherent system and its applications in reliability. In: Soyer R, Mazzuchi T, Singpurwalla N (eds) Mathematical reliability: an expository perspective. Kluwer, Boston, pp 3–29
7. Boland PJ, Samaniego FJ, Vestrup EM (2003) Linking dominations and signatures in network reliability theory. In: Lindqvist BH, Doksum K (eds) Mathematical and statistical methods in reliability. World Scientific, Singapore, pp 89–103
8. Elperin T, Gertsbakh IB, Lomonosov M (1991) Estimation of network reliability using graph evolution models. IEEE Trans Reliab 40(5):572–581
9. Gertsbakh IB, Shpungin Y (2010) Models of network reliability. CRC Press, Boca Raton
10. Kochar S, Mukerjee H, Samaniego FJ (1999) The ‘‘signature’’ of a coherent system and its application to comparisons among systems. Naval Res Logist 46(5):507–523
11. Marichal JL, Mathonet P (2011) System signatures for dependent lifetimes: explicit expression and interpretations. J Multivar Anal 102(5):931–936
12. Navarro J, Eryilmaz S (2007) Mean residual lifetimes of consecutive-k-out-of-n systems. J Appl Prob 44(1):82–98
13. Navarro J, Rychlik T (2007) Reliability and expectation bounds for coherent systems with exchangeable components. J Multivar Anal 98(1):102–113
14. Navarro J, Shaked M (2006) Hazard rate ordering of order statistics and systems. J. Appl Probab 43(2):391-408
15. Navarro J, Spizzichino F (2010a) On the relationships between copulas of order statistics and marginal distributions. Stat Prob Lett 80:473-479
16. Navarro J, Spizzichino F (2010b) Comparisons of series and parallel systems with components sharing the same copula. Appl Stoch Models Bus Ind 26(6):775-791
17. Navarro J, Samaniego FJ, Balakrishnan N, Bhattacharaya D (2008) On the application and extension of system signatures in engineering reliability. Nav Res Log 55(4):313-327
18. Navarro J, Spizzichino F, Balakrishnan N (2010) Applications of average and projected systems to the study of coherent systems. J Multivar Anal 101(6):1471-1482
19. Nelsen R (2006) An introduction to copulas. Springer, New York
20. Samaniego FJ (1985) On closure of the IFR class under formation of coherent systems. IEEE Trans Reliab 34(1):69-72
21. Samaniego FJ (2007) System signatures and their application in engineering reliability. Springer, Berlin
22. Satyanarayana A, Prabhakar A (1978) New topological formula and rapid algorithm for reliability analysis of complex networks. IEEE Trans Reliab 27(2):82-100
23. Spizzichino F (2008) The role of signature and symmetrization for systems with non-exchangeable components. In: Bedford T, Quigley J, Walls L, Alkali B, Daneshkhah A, Hardman G (eds) Mathematical modeling for reliability. IOS Press, Amsterdam, pp 138-148