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RELATIONSHIPS BETWEEN IMPORTANCE MEASURES AND REDUNDANCY IN SYSTEMS WITH DEPENDENT COMPONENTS

  • Jorge Navarro (a1), Pedro Fernández-Martínez (a1), Juan Fernández-Sánchez (a2) and Antonio Arriaza (a3)

Abstract

The paper shows the connections between some importance indices for the components in an engineering coherent system and the performance of the system obtained when a redundancy mechanism is applied to a specific component. A copula approach is used to model the dependency among the components. This approach includes the popular case of independent components. Under some assumptions, it is proved that if component i is more important than component j, then the system obtained by applying a redundancy procedure to the ith component is better, under different stochastic criteria, than that obtained with the jth component. These results can be applied to several redundancy mechanisms. A new importance index is defined to study active redundancies. Some illustrative examples are provided.

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1.Arriaza, A., Navarro, J., & Suárez-Llorens, A. (2018). Stochastic comparisons of replacement policies in coherent systems under minimal repair. Naval Research Logistics 65: 550565.
2.Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing. International Series in Decision Processes. New York: Holt, Rinehart and Winston, Inc.
3.Belzunce, F., Martínez-Riquelme, C., & Ruiz, J.M. (2018). Allocation of a relevation in redundancy problems. To appear in Applied Stochastic Models in Business and Industry. Published online first April 6, 2018. DOI: 10.1002/asmb.2328.
4.Burkschat, M. & Navarro, J. (2018). Stochastic comparisons of systems based on sequential order statistics via properties of distorted distributions. Probability in the Engineering and Informational Sciences 32: 246274.
5.Calì, C., Longobardi, M., & Navarro, J. (2018). Properties for generalized cumulative past measures of information. To appear in Probability in the Engineering and Informational Sciences. Published online first October 29, 2018. DOI: 10.1017/S0269964818000360.
6.Durante, F. & Sempi, C. (2016). Principles of Copula Theory. London: CRC/Chapman & Hall.
7.Durante, F., Saminger-Platz, S., & Sarkoci, P. (2009). Rectangular patchwork for bivariate copulas and tail dependence. Communications in Statistics Theory and Methods 38: 25152527.
8.Federer, H. (1969). Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften 153. Berlin-Heidelberg-New York: Springer-Verlag.
9.Gertsbakh, I.B. & Shpungin, Y. (2012). Combinatorial approach to computing component importance indexes in coherent systems. Probability in the Engineering and Informational Sciences 26: 117128.
10.Hazra, N.K. & Nanda, A.K. (2014). Component redundancy versus system redundancy in different stochastic orderings. IEEE Transactions on Reliability 63: 567582.
11.Iyer, S. (1992). The Barlow–Proschan importance and its generalizations with dependent components. Stochastic Processes and their Applications 42: 353359.
12.Krakowski, M. (1973). The relevation transform and a generalization of the Gamma distribution function. Revue française d'automatique, informatique, recherche opérationnelle, tome 7 (no. V-2): 107120.
13.Kuo, W. & Zhu, X. (2012). Importance measures in reliability, risk, and optimization. Principles and applications. West Sussex, UK: John Wiley & Sons Ltd.
14.Marichal, J.-L. & Mathonet, P. (2013). On the extensions of Barlow–Proschan importance index and system signature to dependent lifetimes. Journal of Multivariate Analysis 115: 4856.
15.Miziuła, P. & Navarro, J. (2017). Sharp bounds for the reliability of systems and mixtures with ordered components. Naval Research Logistics 64: 108116.
16.Miziuła, P. & Navarro, J. (2019). A new importance measure for reliability systems with dependent components. To appear in IEEE Transactions on Reliability, Published online first February 2019. DOI: 10.1109/TR.2019.2895400.
17.Navarro, J. & Gómis, M.C. (2016). Comparisons in the mean residual life order of coherent systems with identically distributed components. Applied Stochastic Models in Business and Industry 32: 3347.
18.Navarro, J., del Águila, Y., Sordo, M.A., & Suárez-Llorens, A. (2013). Stochastic ordering properties for systems with dependent identically distributed components. Applied Stochastic Models in Business and Industry 29: 264278.
19.Navarro, J., del Águila, Y., Sordo, M.A., & Suárez-Llorens, A. (2016). Preservation of stochastic orders under the formation of generalized distorted distributions. Applications to coherent systems. Methodology and Computing in Applied Probability 18: 529545.
20.Nelsen, R.B. (2006). An introduction to copulas, 2nd ed., New York: Springer.
21.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. Springer series in statistics. New York: Springer.
22.Zhang, X. & Wilson, A. (2017). System reliability and component importance under dependence. Technometrics 59: 215224.

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