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Algorithms and Formulae for Conversion Between System Signatures and Reliability Functions

Part of: Operations research and management science Survival analysis and censored data Circuits, networks

Published online by Cambridge University Press:  30 January 2018

Jean-Luc Marichal
Jean-Luc Marichal*
Affiliation:
University of Luxembourg
*
∗ Postal address: Mathematics Research Unit, FSTC, University of Luxembourg, 6, rue Coudenhove-Kalergi, L-1359 Luxembourg, Luxembourg. Email address: [email protected]
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Abstract

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The concept of a signature is a useful tool in the analysis of semicoherent systems with continuous, and independent and identically distributed component lifetimes, especially for the comparison of different system designs and the computation of the system reliability. For such systems, we provide conversion formulae between the signature and the reliability function through the corresponding vector of dominations and we derive efficient algorithms for the computation of any of these concepts from any other. We also show how the signature can be easily computed from the reliability function via basic manipulations such as differentiation, coefficient extraction, and integration.

Keywords

Semicoherent systemsystem signaturereliability functiondomination vector

MSC classification

Primary: 62N05: Reliability and life testing 90B25: Reliability, availability, maintenance, inspection
Secondary: 94C10: Switching theory, application of Boolean algebra; Boolean functions
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 2 , June 2015 , pp. 490 - 507
Copyright
© Applied Probability Trust 

References

Barlow, R. E. and Iyer, S. (1988). Computational complexity of coherent systems and the reliability polynomial. Prob. Eng. Inf. Sci. 2, 461–469.Google Scholar
Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
Boland, P. J. (2001). Signatures of indirect majority systems. J. Appl. Prob. 38, 597–603.Google Scholar
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 (Ser. Qual. Reliab. Eng. Statist. 7), World Scientific, River Edge, NJ, pp. 89–103.Google Scholar
Gertsbakh, I., Shpungin, Y. and Spizzichino, F. (2011). Signatures of coherent systems built with separate modules. J. Appl. Prob. 48, 843–855.CrossRefGoogle Scholar
Marichal, J.-L. (2006). Cumulative distribution functions and moments of lattice polynomials. Statist. Prob. Lett. 76, 1273–1279.Google Scholar
Marichal, J.-L. and Mathonet, P. (2011). Extensions of system signatures to dependent lifetimes: explicit expressions and interpretations. J. Multivariate Anal. 102, 931–936.Google Scholar
Marichal, J.-L. and Mathonet, P. (2013). Computing system signatures through reliability functions. Statist. Prob. Lett. 83, 710–717.Google Scholar
Ramamurthy, K. G. (1990). Coherent Structures and Simple Games (Theory Decision Library Ser. C Game Theory Math. Prog. Operat. Res. 6). Kluwer, Dordrecht.Google Scholar
Samaniego, F. J. (1985). On closure of the IFR class under formation of coherent systems. IEEE Trans. Reliab. 34, 69–72.Google Scholar
Samaniego, F. J. (2007). {System Signatures and Their Applications in Engineering Reliability} (Internat. Ser. Operat. Res. Manag. Sci. 110). Springer, New York.Google Scholar