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On the behaviour of some new ageing properties based upon the residual life of k-out-of-n systems

Part of: Special processes Distribution theory

Published online by Cambridge University Press:  14 July 2016

Xiaohu Li  and
Ming J. Zuo
Xiaohu Li*
Affiliation:
Lanzhou University
Ming J. Zuo*
Affiliation:
University of Alberta
*
∗ Postal address: Department of Mathematics, Lanzhou University, Lanzhou 730000, China. Email address: xhli@lzu.edu.cn
∗∗ Postal address: Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G8.
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Abstract

In this paper, we investigate k-out-of-n systems with independent and identically distributed components. Some characterizations of the IFR(2), DMRL, NBU(2) and NBUC classes of life distributions are obtained in terms of the monotonicity of the residual life given that the (n-k)th failure has occurred at time t ≥ 0. These results complement those reported by Belzunce, Franco and Ruiz (1999). Similar conclusions based on the residual life of a parallel system conditioned by the (n-k)th failure time are presented as well.

Keywords

DMRLIFR(2)NBUCNBU(2)NBULtincreasing convex orderincreasing concave orderparallel systemresidual life

MSC classification

Primary: 62E10: Characterization and structure theory
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 426 - 433
Copyright
Copyright © Applied Probability Trust 2002 

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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
Belzunce, E. M., Ortega, M., and Ruiz, J. M. (2001). A note on stochastic comparisons of excess lifetimes of renewal processes. J. Appl. Prob. 38, 747–753.CrossRefGoogle Scholar
Belzunce, F., Franco, M., and Ruiz, J. M. (1999). On aging properties based on the residual life of k-out-of-n systems. Prob. Eng. Inf. Sci. 13, 193–199.CrossRefGoogle Scholar
Cao, J., and Wang, Y. (1991). The NBUC and NWUC classes of life distributions. J. Appl. Prob. 28, 473–479. (Correction: 29 (1992), 753.)CrossRefGoogle Scholar
Cao, J., and Wang, Y. (1992). Correction for ‘The NBUC and NWUC classes of life distributions’. J. Appl. Prob. 29, 753.Google Scholar
Chen, Y. (1994). Classes of life distributions and renewal counting process. J. Appl. Prob. 31, 1110–1115.CrossRefGoogle Scholar
Deshpande, J. V., Kochar, S. C., and Singh, H. (1986). Aspects of positive ageing. J. Appl. Prob. 23, 748–758.CrossRefGoogle Scholar
Franco, M., Ruiz, J. M., and Ruiz, M. C. (2001). On closure of the IFR(2) and NBU(2) classes. J. Appl. Prob. 38, 235–241.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.CrossRefGoogle Scholar
Hollander, M., and Proschan, F. (1984). Nonparametric concepts and methods in reliability. In Handbook of Statistics, Vol. 4, Nonparametric Methods, eds Krishnaiah, P. R. and Sen, P. K., North-Holland, Amsterdam, pp. 613–655.Google Scholar
Langberg, N. A., Leon, R. V., and Proschan, F. (1980). Characterizations of nonparametric classes of life distributions. Ann. Prob. 8, 1163–1170.CrossRefGoogle Scholar
Li, X., and Kochar, S. (2001). Some new results involving the NBU(2) classes of life distributions. J. Appl. Prob. 38, 242–247.CrossRefGoogle 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
Pellerey, F., and Petakos, K. (2002). On closure property of the NBUC class under formation of parallel systems. Tech. Rep., Università di Bergamo. To appear in IEEE Trans. Reliab.CrossRefGoogle Scholar
Shaked, M., and Shanthikumar, J. G. (1994). Stochastic Orders and Their Applications. Academic Press, San Diego, CA.Google Scholar
Stoyan, D. (1983). Comparison Methods for Queues and Other Stochastic Models. John Wiley, New York.Google Scholar