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On the Signatures of Ordered System Lifetimes

Part of: Operations research and management science Special processes Nonparametric inference

Published online by Cambridge University Press:  30 January 2018

N. Balakrishnan  and
William Volterman
N. Balakrishnan*
Affiliation:
McMaster University
William Volterman*
Affiliation:
McMaster University
*
∗ Postal address: Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada.
∗ Postal address: Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada.
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Abstract

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The idea of the system signature is extended here to the case of ordered system lifetimes arising from a test of coherent systems with a signature. An expression is given for the computation of the ordered system signatures in terms of the usual system signature for system lifetimes. Some properties of the ordered system signatures are then established. Closed-form expressions for the ordered system signatures are obtained in some special cases, and some illustrative examples are presented.

Keywords

Coherent systemorder statisticssystem signature

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 90B25: Reliability, availability, maintenance, inspection 62G30: Order statistics; empirical distribution functions
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 1 , March 2014 , pp. 82 - 91
Copyright
© Applied Probability Trust 

References

Balakrishnan, N., Ng, H. K. T. and Navarro, J. (2011). Exact nonparametric inference for component lifetime distribution based on lifetime data from systems with known signatures. J. Nonparametric Statist. 23, 741–752.CrossRefGoogle Scholar
Boland, P. J. and Samaniego, F. (2004). The signature of a coherent system and its applications in reliability. In Mathematical Reliability: An Expository Perspective. eds Soyer, R., Mazzuchi, T., and Singpurwalla, N. D., Kluwer, Boston, MA, pp. 3–30.CrossRefGoogle Scholar
Cramer, E. (2002). A note on moments of progressively type II censored order statistics. Commun. Statist. Theory Meth. 31, 1301–1307.CrossRefGoogle 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
Kochar, S., Mukerjee, H. and Samaniego, F. J. (1999). The ‘signature’ of a coherent system and its application to comparisons among systems. Naval Res. Logistics 46, 507–523.3.0.CO;2-D>CrossRefGoogle Scholar
Samaniego, F. J. (1985). On closure of the IFR class under formation of coherent systems. IEEE Trans. Reliab. R-34, 69–72.CrossRefGoogle Scholar
Samaniego, F. J. (2007). System Signatures and Their Applications in Engineering Reliability (Internat. Ser. Operat. Res. Management Sci. 110). Springer, New York.CrossRefGoogle Scholar
Shaked, M. and Suarez-Llorens, A. (2003). On the comparison of reliability experiments based on the convolution order. J. Amer. Statist. Assoc. 98, 693–702.CrossRefGoogle Scholar
Spizzichino, F. and Navarro, J. (2012). Signatures and symmetry properties of coherent systems. In Recent Advances in System Reliability, eds Lisnianski, A. and Frenkel, I., Springer, London, pp. 33–48.CrossRefGoogle Scholar