Hostname: page-component-89b8bd64d-72crv Total loading time: 0 Render date: 2026-05-08T04:10:25.565Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE BEHAVIORS OF THE PERCENTILE RESIDUAL LIFE FOR COMPONENTS AND FOR K-OUT-OF-N SYSTEMS

Published online by Cambridge University Press:  20 January 2015

Yan Shen  and
Zhisheng Ye
Yan Shen
Affiliation:
Department of Statistics, School of Economics, Xiamen University, Fujian, China E-mail: sheny@xmu.edu.cn
Zhisheng Ye
Affiliation:
Department of Industrial and Systems Engineering, National University of Singapore, Singapore E-mail: yez@nus.edu.sg
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper investigates properties of the percentile residual life (PRL) function for a single component and for a k-out-of-n system. The shape of the component PRL function can be determined by the component failure rate function. The intimate relations between these two functions are studied first. Then we generalize the results to a k-out-of-n system by assuming independent and identical components. We show that the behavior of the PRL for a k-out-of-n system is quite different from the component PRL. We also find that for series and parallel systems, the location of the change point of the PRL is monotone in the number of components in a system.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 2 , April 2015 , pp. 291 - 308
Copyright
Copyright © Cambridge University Press 2015 

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.)

Article purchase

Temporarily unavailable

References

1.Arnold, B.C. & Brockett, P.L. (1983). When does the βth percentile residual life function determine the distribution? Operations Research 31: 391–396.CrossRefGoogle Scholar
2.Asadi, M. & Bayramoglu, I. (2006). The mean residual life function of a k-out-of-n structure at the system level. IEEE Transactions on Reliability 55(2): 314–318.CrossRefGoogle Scholar
3.Bebbingon, M., Lai, C.D. & Ričardas, Z. (2007). Bathtub-type curves in reliability and beyond. Australian & New Zealand Journal of Statistics 49(3): 251–265.Google Scholar
4.Chung, C.J.F. (1989). Confidence bands for percentile residual lifetimes under random censorship model. Journal of Multivariate Analysis 29: 94–126.Google Scholar
5.Csörgö, M. & Csörgö, S. (1987). Estimation of percentile residual life. Operations Research 35: 598–606.Google Scholar
6.Franco-Pereira, A.M., Lillo, R.E. & Shaked, M. (2012). The decreasing percentile residual life ageing notion. Statistics 46(5): 587–603.Google Scholar
7.Hemmati, F., Khorram, E. & Rezakhah, S. (2011). A new three-parameter ageing distribution. Journal of Statistical Planning and Inference 141(7): 2266–2275.Google Scholar
8.Hu, T., Jin, W. & Khaledi, B.E. (2007). Ordering conditional distributions of generalized order statistics. Probability in the Engineering and Informational Science 21(3): 401–417.Google Scholar
9.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 Science 15(2): 259–272.Google Scholar
10.Jeong, J. & Fine, J.P. (2013). Nonparametric inference on cause-specific quantile residual life. Biometrical Journal 55(1): 68–81.CrossRefGoogle ScholarPubMed
11.Joe, H. (1985). Characterization of life distributions from percentile residual lifetimes. Annals of the Institute of Statistical Mathematics 37: 165–172.Google Scholar
12.Joe, H. & Proschan, F. (1984). Comparisons of two life distributions on the basis of their percentile residual life functions. Canadian Journal of Statistics 12: 91–97.Google Scholar
13.Joe, H. & Proschan, F. (1984). Percentile residual life functions. Operations Research 32: 668–678.Google Scholar
14.Khaledi, B.E. & Shaked, M. (2007). Ordering conditional lifetimes of coherent systems. Journal of Statistical Planning and Inference 137: 1173–1184.Google Scholar
15.Lai, C.D., Xie, M. & Murthy, D.N.P. (2003). A modified Weibull distribution. IEEE Transactions on Reliability 52(1): 33–37.CrossRefGoogle Scholar
16.Li, X. & Zhao, P. (2006). Some aging properties of the residual life of k-out-of-n systems. IEEE Transactions on Reliability 55(3): 535–541.Google Scholar
17.Lillo, R.E. (2005). On the median residual lifetime and its aging properties: a characterization theorem and applications. Naval Research Logistics 52(4): 370–380.Google Scholar
18.Poursaeed, M.H. (2010). A note on the mean past and the mean residual life of a (n−k+1)-out-of-n system under multi-monitoring. Statistical Papers 51: 409–419Google Scholar
19.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
20.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic Orders. New York: Springer.Google Scholar
21.Ye, Z.S., Tang, L.C. & Xie, M. (2011). A burn-in scheme based on percentiles of the residual life. Journal of Quality Technology 43(4): 334–345.Google Scholar
22.Ye, Z.S., Murthy, D. N.P., Xie, M. & Tang, L.C. (2013). Optimal burn-in for repairable products sold with a two-dimensional warranty. IIE Transactions 45(2): 164–176.Google Scholar
23.Zhang, Z. (2011). Ordering new conditional residual lifetimes of k-out-of-n systems. Communications in Statistics – Theory and Methods 40: 1591–1600.Google Scholar