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Some new results involving the NBU(2) class of life distributions

Part of: Special processes Distribution theory

Published online by Cambridge University Press:  14 July 2016

Xiaohu Li  and
Subhash C. Kochar
Xiaohu Li*
Affiliation:
Lanzhou University
Subhash C. Kochar*
Affiliation:
Indian Statistical Institute, Delhi
*
∗ Postal address: Department of Mathematics, Lanzhou University, Lanzhou 730000, Gansu Province, China. Email address: [email protected]
∗∗ Postal address: Statistics and Mathematics Unit, Indian Statistical Institute, 7, S.J.S. Sansanwal Marg, New Delhi 110016, India.
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Abstract

Some new results about the NBU(2) class of life distributions are obtained. Firstly, it is proved that the decreasing with time of the increasing concave ordering of the excess lifetime in a renewal process leads to the NBU(2) property of the interarrival times. Secondly, the NBU(2) class of life distributions is proved to be closed under the formation of series systems. Finally, it is also shown that the NBU(2) class is closed under convolution operation.

Keywords

convolutionexcess lifetimeNBU(2)series systems

MSC classification

Primary: 62E10: Characterization and structure theory
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 1 , March 2001 , pp. 242 - 247
Copyright
Copyright © by the Applied Probability Trust 2001 

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References

Barlow, R. E., and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.Google Scholar
Bryson, M. C., and Siddiqui, M. M. (1969). Some criterias for aging. J. Amer. Statist. Assoc. 64, 1472–1483.CrossRefGoogle Scholar
Cao, J., and Wang, Y. (1991). The NBUC and NWUC classes of life distributions. J. Appl. Prob. 28, 473–479.Google Scholar
Chen, Y. (1994). Classes of life distributions and renewal counting process. J. Appl. Prob. 31, 1110–1115.Google Scholar
Deshpande, J. V., Kochar, S. C., and Singh, H. (1986). Aspects of positive ageing. J. Appl. Prob. 23, 748–758.CrossRefGoogle Scholar
Grosh, D. L. (1982). A parallel system of CFR units is IFR. IEEE Trans. Rel. 31, 403.CrossRefGoogle Scholar
Hendi, M. I., Mashhour, A. F., and Montasser, M. A. (1993). Closure of the NBUC class under formation of parallel systems. J. Appl. Prob. 30, 975–978.Google Scholar
Karlin, S., and Taylor, H. M. (1975). A First Course in Stochastic Processes, 2nd edn. Academic Press, New York.Google Scholar
Klefsjö, B. (1982). The HNBUE and HNWUE classes of life distributions. Naval Res. Logist. Quart. 29, 331–344.Google Scholar
Li, X., Li, Z., and Jing, B. (2000). Some results about the NBUC class of life distributions. Statist. Prob. Lett. 46, 229–237.CrossRefGoogle Scholar
Shaked, M., and Shanthikumar, J. G. (1994). Stochastic Orders and Their Applications. Academic Press, San Diego.Google Scholar