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Applicable Algebra in Engineering, Communication and Computing

02.07.2024 | Original Paper

Stable coherent systems

verfasst von: Rodrigo Iglesias, Fatemeh Mohammadi, Patricia Pascual-Ortigosa, Eduardo Sáenz-de-Cabezón, Henry P. Wynn

Erschienen in: Applicable Algebra in Engineering, Communication and Computing

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Abstract

We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of stable systems can be efficiently computed using the algebraic versions of improved inclusion-exclusion formulas and sum of disjoint products.

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Literatur
1.
Abbott, J., Bigatti, A.M.: CoCoALib: a C++ library for doing computations in commutative algebra. http://cocoa.dima.unige.it/cocoalib
2.
Abraham, J.A.: An improved algorithm for network reliability. IEEE Trans. Reliab. R–28(1), 58–61 (1979)CrossRef
3.
Alberelli, D., Lella, P.: Strongly stable ideals and Hilbert polynomials. J. Softw. Algebra Geom. 9, 1–9 (2019)MathSciNetCrossRef
4.
Aramova, A., Herzog, J., Hibi, T.: Weakly stable ideals. Osaka J. Math. 34, 745–745 (1997)MathSciNet
5.
6.
Bigatti, A.M., Pascual-Ortigosa, P., Sáenz-de Cabezón, E.: A C++ class for multi-state algebraic reliability computations. Reliab. Eng. Syst. Saf. 213, 107751 (2021)CrossRef
7.
Birnbaum, A.: Some latent trait models and their use in inferring an examinee’s ability. In: Statistical Theories of Mental Test Scores (1968)
8.
Birnbaum, Z.W.: On the importance of different components in a multicomponent system. In: Multivariate Analysis, Vol. 2, pp. 581–592. Academic Press (1969)
9.
Boedigheimer, R.A., Kapur, K.C.: Optimal arrangement of components via pairwise rearrangements. IEEE Trans. Rel. 43, 46–50 (1994)CrossRef
10.
Ceria, M.L.: Barcode vs. Janet tree. Atti Accad. Peloritana dei Pericolanti 97:1–12 (2019)
11.
DiPasquale, M., Francisco, C.A., Mermin, J., Schweig, J., Sosa, G.: The Rees algebra of a two-Borel ideal is Koszul. Proc. Am. Math. Soc. 147, 467–479 (2019)MathSciNetCrossRef
12.
Dohmen, K.: Improved Bonferroni inequalities Via Abstract Tubes. Springer, Berlin (2003)CrossRef
13.
14.
15.
16.
17.
Gerdt, V.P., Blinkov, Y.A., Yanovich, D.A.: Construction of janet bases i. monomial bases. In: Computer Algebra in Scientific Computing-CASC 2001, pp. 233–247. Springer (2001)
18.
Giglio, B., Wynn, H.P.: Monomial ideals and the Scarf complex for coherent systems in reliability theory. Ann. Stat. 32, 1289–1311 (2004)MathSciNetCrossRef
19.
Grayson, D.R., Stillman, M.E.: Macaulay2, a software system for research in algebraic geometry. http://www.math.uiuc.edu/Macaulay2/
20.
Huang, D.-H., Chang, P.-C., Lin, Y.-K.: A multi-state network to evaluate network reliability with maximal and minimal capacity vectors by using recursive sum of disjoint products. Expert Syst. Appl. 193, 116421 (2022)CrossRef
21.
Iglesias, R., Pascual-Ortigosa, P., Sáenz-De-Cabezón, E.: An algebraic version of the sum-of-disjoint-products method for multi-state system reliability analysis. In: Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, 2022, pp. 509–516. ACM (2022)
22.
Iglesias, R., Sáenz-de-Cabezón, E.: Janet-stable ideals and componentwise linearity (in preparation) (2024)
23.
Kuo, W., Zhu, X.: Importance Measures in Reliability, Risk and Optimization. Wiley, New York (2012)CrossRef
24.
Kuo, W., Zuo, M.: Optimal Reliability Modelling: Principles and Applications. Wiley, New York (2003)
25.
Kuo, W., Zhu, X.: Importance Measures in Reliability, Risk, and Optimization: Principles and Applications. Wiley, New York (2012)CrossRef
26.
Levitin, G.: The Universal Generating Function in Reliability Analysis and Optimization. Springer, Berlin (2005)
27.
Luo, T., Trivedi, K.: An improved algorithm for coherent-system reliability. IEEE Trans. Reliab. 47(1), 73–78 (1998)CrossRef
28.
Meng, F.C.: Comparing the importance of system components by some structural characteristics. IEEE Trans. Reliab. 45, 59–65 (1996)CrossRef
29.
Mo, Y., Liudong, X., Amari, S.V., Dugan, J.B.: Efficient analysis of multi-state k-out-of-n systems. Reliab. Eng. Syst. Saf. 133, 95–105 (2015)CrossRef
30.
Mohammadi, F., Pascual-Ortigosa, P., Sáenz-de-Cabezón, E., Wynn, H.P.: Polarization and depolarization of monomial ideals with application to multi-state system reliability. J. Algebraic Combin. 51, 617–639 (2020)MathSciNetCrossRef
31.
Mohammadi, F., Sáenz-de Cabezón, E., Wynn, H.P.: Efficient multicut enumeration of k-out-of-n:f and consecutive k-out-of-n:f systems. Pattern Recognit. Lett. 102, 82–88 (2018)CrossRef
32.
Pascual-Ortigosa, P., Sáenz-de-Cabezón, E.: Algebraic analysis of variants of multi-state k-out-of-n systems. Mathematics 9(17) (2021)
33.
Pascual-Ortigosa, P., Sáenz-de-Cabezón, E., Wynn, H.P.: Algebraic reliability of multi-state \(k\)-out-of-\(n\) systems. Probab. Eng. Inf. Sci. 35, 903–927 (2021)MathSciNetCrossRef
34.
Ramírez-Márquez, J.E., Coit, D.W.: Composite importance measures for multi-state systems with multi-state components. IEEE Trans. Reliab. 54, 517–529 (2005)CrossRef
35.
Ramírez-Márquez, J.E., Rocco, C.M., Gebre, B.A., Coit, D.W., Tortorella, M.: New insights on multi-state component criticallity and importance. Reliab. Eng. Syst. Saf. 894–904 (2006)
36.
37.
Sáenz-de-Cabezón, E.: Multigraded betti numbers without computing minimal free resolutions. Appl. Alg. Eng. Commun. Comput. 20, 481–495 (2009)MathSciNetCrossRef
38.
Sáenz-de-Cabezón, E., Wynn, H.P.: Betti numbers and minimal free resolutions for multi-state system reliability bounds. J. Symb. Comput. 44, 1311–1325 (2009)MathSciNetCrossRef
39.
Sáenz-de-Cabezón, E., Wynn, H.P.: Algebraic reliability of two-terminal networks. Appl. Alg. Eng. Commun. Comput. 21, 443–457 (2010)CrossRef
40.
Sáenz-de-Cabezón, E., Wynn, H.P.: Hilbert functions for design in reliability. IEEE Trans. Reliab. 64, 83–93 (2015)CrossRef
41.
Seiler, W.M.: A combinatorial approach to involution and \(\delta\)-regularity i: involutive bases in polynomial algebras of solvable type. Appl. Algebra Eng. Commun. Comput. 20, 207–259 (2009)MathSciNetCrossRef
42.
Seiler, W.M.: A combinatorial approach to involution and \(\delta\)-regularity ii: Structure analysis of polynomial modules with Pommaret bases. Appl. Algebra Eng. Commun. Comput. 20, 261–338 (2009)MathSciNetCrossRef
43.
44.
45.
Trivedi, K.S., Bobbio, A.: Reliability and Availability Engineering. Cambridge University Press, Cambridge (2017)CrossRef
46.
Xing, J., Feng, C., Qian, X., Dai, P.: A simple algorithm for sum of disjoint products. In: 2012 Proceedings Annual Reliability and Maintainability Symposium, pp. 1–5 (2012)
47.
Yeh, W.C.: An improved sum-of-disjoint-products technique for symbolic multi-state flow network reliability. IEE Trans. Reliab. 64, 1185–1193 (2015)CrossRef
Metadaten
Titel
Stable coherent systems
verfasst von
Rodrigo Iglesias
Fatemeh Mohammadi
Patricia Pascual-Ortigosa
Eduardo Sáenz-de-Cabezón
Henry P. Wynn
Publikationsdatum
02.07.2024
Verlag
Springer Berlin Heidelberg
Erschienen in
Applicable Algebra in Engineering, Communication and Computing
Print ISSN: 0938-1279
Elektronische ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-024-00665-3

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