Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-28T07:16:45.099Z Has data issue: false hasContentIssue false
  • English
  • Français

MONOTONICITY PROPERTIES OF RESIDUAL LIFETIMES OF PARALLEL SYSTEMS AND INACTIVITY TIMES OF SERIES SYSTEMS WITH HETEROGENEOUS COMPONENTS

Published online by Cambridge University Press:  25 November 2011

Weiyong Ding ,
Xiaohu Li  and
Narayanaswamy Balakrishnan
Weiyong Ding
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
Xiaohu Li
Affiliation:
School of Mathematical Science, Xiamen University, Xiamen 361005, China. E-mail: mathxhli@hotmail.com
Narayanaswamy Balakrishnan
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, CanadaL8S 4K1
Get access Rights & Permissions [Opens in a new window]

Abstract

Here, we discuss the stochastic comparison of residual lifetimes of parallel systems and inactivity times of series systems by means of the reversed hazard rate order when the components of the systems are independent but not necessarily identically distributed. We also establish some monotonicity properties of such residual lifetimes of parallel systems and inactivity times of series systems. These results extend some of the recent results in this direction due to Zhao, Li, and Balakrishnan [21], Kochar and Xu [12], and Saledi and Asadi [16].

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 1 , January 2012 , pp. 61 - 75
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Asadi, M. (2006). On the mean past lifetime of the components of a parallel system. Journal of Statistical Planning and Inference 136: 1197–1206.Google Scholar
2.Asadi, M. & Bairamov, I. (2005). A note on the mean residual life function of a parallel system. Communications in Statistics-Theory and Methods 34: 475–484.Google 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 Its Applications 1: 119–131.Google Scholar
4.Balakrishnan, N. (2007). Permanents, order statistics, outliers, and robustness. Revista Matemátical Complutense 20: 7–107.Google Scholar
5.Balakrishnan, N., Belzunce, F., Hami, N., & Khaledi, B-E. (2010). Univariate and multivariate likelihood ratio ordering of generalized order statistics and associated conditional variables. Probability in the Engineering and Informational Sciences 24: 441–455.Google Scholar
6.Block, H.W., Savits, T.H., & Singh, H. (1998). The reversed hazard rate function. Probability in the Engineering and Informational Sciences 12: 69–90.Google Scholar
7.Bon, J.L. & Păltănea, E. (2006). Comparisons of order statistics in a random sequence to the same statistics with i.i.d. variables. ESAIM: Probability and Statistics 10: 1–10.Google Scholar
8.Chandra, N.N. & Roy, D. (2001). Some results on reversed hazard rate function. Probability in the Engineering and Informational Sciences 15: 95–102.Google Scholar
9.Goliforushani, S., Asadi, M., & Balakrishnan, N. (2011). On the residual and inactivity times of the components of used coherent systems. Journal of Applied Probability (to appear).Google Scholar
10.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.Google Scholar
11.Khaledi, B-E. & Shaked, M. (2007). Ordering conditional residual lifetimes of coherent systems. Journal of Statistical Planning and Inference 137: 1173–1184.Google Scholar
12.Kochar, S. & Xu, M. (2010). On residual lifetimes of k-out-of-n systems with nonidentcial components. Probability in the Engineering and Informational Sciences 24: 109–127.Google Scholar
13.Li, X. & Lu, J. (2003). Stochastic comparisons on residual life and inactivity time of series and parallel systems. Probability in the Engineering and Informational Sciences 17: 267–275.Google 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.Google Scholar
15.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.Google Scholar
16.Saledi, E.T. & Asadi, M. (2010). Results on the past lifetime of (n−k+1)-out-of-n structures with nonidentical components. Metrika doi: 10.1007/s00184-010-0335-3.Google Scholar
17.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.Google Scholar
18.Tavangar, M. & Asadi, M. (2010). A study on the mean past lifetime of the components of (n−k+1)- out-of-n system at the system level. Metrika 72: 59–73.Google Scholar
19.Zhao, P. & Balakrishnan, N. (2009). Stochastic comparisons of conditional generalized order statistics. Journal of Statistical Planning Inference 139: 2920–2932.Google Scholar
20.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.Google Scholar