Abstract
The present paper deals with real-life bridge structure and evaluates the reliability function with the help of the universal generating function technique where the components of the system have different performance states. The bridge system (complex) is known as the combination of series and the parallel system where the system cannot be simplified into pure series or pure parallel structure. Universal generating function technique can find the performance of the system as a whole depends upon the overall performance of the components where these components are independent and identically distributed. Also, expected time Barlow–Proschan index, tail signature and signature of the proposed complex system using Owen’s and Boland methods have been calculated.
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Abbreviations
- U(z):
-
Universal generating function
- E(t)/E(X):
-
Expected lifetime and expected X
- R :
-
Reliability of the system
- P :
-
Probability of the system
- q :
-
Unreliability
- \( \phi (k) \) :
-
Structure function of kth components
- w/W :
-
Signature and tail signature of the proposed system
- S :
-
Number of components of the system
- \( e_{i} \) :
-
Minimal signature of i components
- \( I_{BP} \) :
-
Barlow–Proschan index of the system
References
Bisht S, Singh SB (2019) Signature reliability of binary state node in complex bridge networks using universal generating function. Int J Qual Reliab Manag 36(2):186–201
Boland PJ (2001) Signatures of indirect majority systems. J Appl Probab 38(2):597–603
Eryilmaz S (2012) The number of failed components in a coherent system with exchangeable components. IEEE Trans Reliab 61(1):203–207
Jafary B, Fiondella L (2016) A universal generating function-based multi-state system performance model subject to correlated failures. Reliab Eng Syst Saf 152:16–27
Kumar A, Ram M (2019) Computation interval-valued reliability of sliding window system. Int J Math Eng Manag Sci 4(1):108–115
Kumar A, Singh SB (2018) Signature reliability of linear multi-state sliding window system. Int J Qual Reliab Manag 35(10):2403–2413
Kumar A, Singh SB (2019) Signature A-within-B-from-D/G sliding window system. Int J Math Eng Manag Sci 4(1):95–107
Levitin G (2001) Incorporating common-cause failures into non-repairable multistate series-parallel system analysis. IEEE Trans Reliab 50(4):380–388
Levitin G (2005) The universal generating function in reliability analysis and optimization. Springer, London, p 442. https://doi.org/10.1007/1-84628-245-4
Levitin G, Lisnianski A (2001) A new approach to solving problems of multi-state system reliability optimization. Qual Reliab Eng Int 17(2):93–104
Levitin G, Lisnianski A (2003) Multi-state system reliability analysis and optimization (Universal generating function and genetic algorithm approach). In: Pham H (ed) Handbook of reliability engineering. Springer, London
Marichal JL, Mathonet P (2013) Computing system signatures through reliability functions. Stat Probab Lett 83(3):710–717
Meenkashi K, Singh SB, Kumar A (2019) Reliability analysis of multi-state complex system with multi-state weighted subsystems. Int J Qual Reliab Manag 36(4):552–568
Navarro J, Rubio R (2009) Computations of signatures of coherent systems with five components. Commun Stat Simul Comput 39(1):68–84
Nowak AS (2004) System reliability models for bridge structures. Bull Polish Acad Sci Tech Sci 52(4):321–328
Nowak AS, Collins KR (2012) Reliability of structures. CRC Press, Boca Raton. ISBN 9780429107467
Owen G (1975) Multilinear extensions and the Banzhaf value. Naval Res Log Q 22(4):741–750
Pokorádi L (2015). Failure probability analysis of bridge structure systems. In: 2015 IEEE 10th Jubilee international symposium on applied computational intelligence and informatics, pp 319–322
Samaniego FJ (2007) System signatures and their applications in engineering reliability, vol 110. Springer Science & Business Media, Berlin
Shapley LS (1953) A value for n-person games. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games, vol 2, issue 28. Princeton University Press, Princeton
Shapley LS (1988) A Value for n-person games. In: Roth AE (ed) The Shapley value: essays in honor of Lloyd S. Shapley. Cambridge University Press, Cambridge, pp 31–40
Ushakov IA (1986) A universal generating function. Soviet J Comput Syst Sci 24(5):118–129
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Kumar, A., Tyagi, S. & Ram, M. Signature of bridge structure using universal generating function. Int J Syst Assur Eng Manag 12, 53–57 (2021). https://doi.org/10.1007/s13198-020-01004-8
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DOI: https://doi.org/10.1007/s13198-020-01004-8