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ON RESIDUAL LIFETIMES OF k-OUT-OF-n SYSTEMS WITH NONIDENTICAL COMPONENTS

Published online by Cambridge University Press:  21 December 2009

Subhash Kochar  and
Maochao Xu
Subhash Kochar
Affiliation:
Department of Mathematics and Statistics, Portland State University, Portland, OR 97201 E-mail: [email protected]
Maochao Xu
Affiliation:
Department of Mathematics and Statistics, Portland State University, Portland, OR 97201 E-mail: [email protected]
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Abstract

In this article, mixture representations of survival functions of residual lifetimes of k-out-of-n systems are obtained when the components are independent but not necessarily identically distributed. Then we stochastically compare the residual lifetimes of k-out-of-n systems in one- and two-sample problems. In particular, the results extend some results in Li and Zhao [14], Khaledi and Shaked [13], Sadegh [17], Gurler and Bairamov [7] and Navarro, Balakrishnan, and Samaniego [16]. Applications in the proportional hazard rates model are presented as well.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 1 , January 2010 , pp. 109 - 127
Copyright
Copyright © Cambridge University Press 2009

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References

1.Asadi, M. & Bairamov, I. (2005). A note on the mean residual life function of a parallel system. Communications in Statistics: Theory and Methods 34: 475–485.CrossRefGoogle Scholar
2.Asadi, M. & Bairamov, I. (2006). The mean residual life function of a k-out-of-n structure at the system level. IEEE Transactions on Reliability 55: 314–318.CrossRefGoogle Scholar
3.Bairamov, I., Ahsanullah, M. & Akhundov, I. (2002). A residual life function of a system having parallel or series structures. Journal of Statistical Theory and Application 1: 119–132.Google Scholar
4.Balakrishnan, N. (2007). Permanents, order statistics, outliers, and robustness. Revista Matemática Complutense 20: 7–107.CrossRefGoogle Scholar
5.Bapat, R.B. & Kochar, S.C. (1994). On likelihood-ratio ordering of order statistics. Linear Algebra and Its Applications 199: 281–291.CrossRefGoogle Scholar
6.Boland, P.J., Hollander, M., Joag-Dev, K. & Kochar, S. (1996). Biviariate dependence properties of order statistics. Journal of Multivariate Analysis 56: 75–89.CrossRefGoogle Scholar
7.Gurler, S. & Bairamov, I. (2009). Parallel and k-out-of-n: G systems with nonidentical components and their mean residual life functions. Applied Mathematical Modelling 33: 1116–1125.CrossRefGoogle Scholar
8.Hu, T., Jin, W. & Khaledi, B.-E. (2007). Ordering conditional distributions of generalized order statistics. Probability in the Engineering and Informational Sciences 21: 401–417.CrossRefGoogle Scholar
9.Hu, T., Wang, F. & Zhu, Z. (2006). Stochastic comparisons and dependence of spacings from two samples of exponential random variables. Communications in Statistics: Theory and Methods 35: 979–988.CrossRefGoogle Scholar
10.Hu, T. & Xie, C. (2006). Negative dependence in the balls and bins experiment with applications to order statistics. Journal of Multivariate Analysis 97: 1342–1354.CrossRefGoogle Scholar
11.Hu, T., Zhu, Z. & Wei, Y. (2001). Likelihood ratio and mean residual life orders for order statistics of heterogeneous random variables. Probability in the Engineering and Informational Sciences 15: 259–272.CrossRefGoogle Scholar
12.Khaledi, B.-E. & Kochar, S.C. (2002). Stochastic orderings among order statistics and sample spacings. In Misra, J.C., (ed.) Uncertainty and Optimality-probability, statistics and operations research. Singapore: World Scientific Publications, pp. 167–203.CrossRefGoogle Scholar
13.Khaledi, B.-E. & Shaked, M. (2007). Ordering conditional lifetimes of coherent systems. Journal of Statistical Planning and Inference 137: 1173–1184.CrossRefGoogle Scholar
14.Li, X. & Zhao, P. (2006). Some aging properties of the residual life of k-out-of-n systems. IEEE Transactions on Reliability 55: 535–541.CrossRefGoogle Scholar
15.Nanda, A.K. & Shaked, M. (2001). The hazard rate and the reversed hazard rate orders, with applications to order statistics. Annals of the Institute of Statistical Mathematics 53: 853–864.CrossRefGoogle Scholar
16.Navarro, J., Balakrishnan, N. & Samaniego, F.J. (2008). Mixture representations of residual lifetimes of used systems. Journal of Applied Probability 45: 1097–1112.CrossRefGoogle Scholar
17.Sadegh, M.K. (2008). Mean past and mean residual life functions of a parallel system with nonidentical components. Communications in Statistics Theory and Methods 37: 1134–1145.CrossRefGoogle Scholar
18.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders and their applications. New York: Springer.Google Scholar
19.Zhao, P., Li, X. & Balakrishnan, N. (2008). Conditional ordering of k-out-of-n systems with independent but nonidentical components. Journal of Applied Probability 45: 1113–1125.CrossRefGoogle Scholar