Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T08:08:08.575Z Has data issue: false hasContentIssue false
  • English
  • Français

Conditional Ordering of k-out-of-n Systems with Independent But Nonidentical Components

Part of: Special processes Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Peng Zhao ,
Xiaohu Li  and
N. Balakrishnan
Peng Zhao*
Affiliation:
Lanzhou University
Xiaohu Li*
Affiliation:
Lanzhou University
N. Balakrishnan*
Affiliation:
McMaster University
*
∗Postal address: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China.
∗Postal address: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China.
∗∗∗∗Postal address: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1. Email address: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

By considering k-out-of-n systems with independent and nonidentically distributed components, we discuss stochastic monotone properties of the residual life and the inactivity time. We then present some stochastic comparisons of two systems based on the residual life and inactivity time.

Keywords

Hazard rate orderinactivity timelikelihood ratio orderresidual lifereversed hazard rate orderstochastic order

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 4 , December 2008 , pp. 1113 - 1125
Copyright
Copyright © Applied Probability Trust 2008 

References

Asadi, M. (2006). On the mean past lifetime of the components of a parallel system. J. Statist. Planning Infer. 136, 1197–1206.CrossRefGoogle Scholar
Asadi, M. and Bairamov, I. (2005). A note on the mean residual life function of a parallel system. Commun. Statist. Theory Meth. 34, 475–484.Google Scholar
Bairamov, I., Ahsanullah, M. and Akhundov, I. (2002). A residual life funtion of a system having parallel or series structures. J. Statist. Theory Appl. 1, 119–131.Google Scholar
Balakarishnan, N. (2007). Permanents, order statistics, outliers, and robustness. Revista Matemàtica Complutense 20, 7–107.Google Scholar
Bapat, R. B. and Beg, M. I. (1989). Order statistics for nonidentically distributed variables and permanents. Sankhyā A 51, 79–93.Google Scholar
Bapat, R. B. and Kochar, S. C. (1994). On likelihood-ratio ordering of order statistics. Linear Algebra Appl. 199, 281–291.Google Scholar
Belzunce, F., Franco, M. and Ruiz, J. M. (1999). On ageing properties based on the residual life of k-out-of-n systems. Prob. Eng. Inf. Sci. 13, 193–199.Google Scholar
Boland, P. J., Hu, T., Shaked, M. and Shanthikumar, J. G. (2002). Stochastic ordering of order statistics. II. In Modeling Uncertainty: An Examination of Stochastic Theory, Methods and Applications, eds Dror, M., L'Ecuyer, P. and Szidarovszky, F., Kluwer, Boston, MA, pp. 607–623.CrossRefGoogle Scholar
David, H. A. and Nagaraja, H. N. (2003). Order Statistics, 3rd edn. John Wiley, Hoboken, NJ.CrossRefGoogle Scholar
Gasemyr, J. and Natvig, B. (1998). The posterior distribution of the parameters of component lifetimes based on autopsy data in a shock model. Scand. J. Statist. 25, 271–292.Google Scholar
Gasemyr, J. and Natvig, B. (2001). Bayesian inference based on partial monitoring of components with applications to preventive system maintenance. Naval Res. Logistics 48, 551–577.Google Scholar
Hu, T. and Zhu, Z. (2003). Stochastic comparisons of order statistics from two samples. Southeast Asian Bull. Math. 27, 89–98.Google Scholar
Hu, T., Jin, W. and Khaledi, B.-E. (2007). Ordering conditional distributions of generalized order statistics. Prob. Eng. Inf. Sci. 21, 401–417.Google Scholar
Hu, T., Wang, F. and Zhu, Z. (2006). Stochastic comparisons and dependence of spacings from two samples of exponential random variables. Commun. Statist. Theory Meth. 35, 979–988.CrossRefGoogle Scholar
Khaledi, B-E. and Shaked, M. (2006). Ordering conditional residual lifetimes of coherent systems. J. Statist. Planning Infer. 137, 1173–1184.CrossRefGoogle Scholar
Kuo, W. and Zuo, M. J. (2002). Optimal Reliability Modeling: Principles and Applications. John Wiley, Hoboken, NJ.Google Scholar
Langberg, N. A., Leon, R. V. and Proschan, F. (1980). Characterization of nonparametric classes of life distributions. Ann. Prob. 8, 1163–1170.Google Scholar
Li, X. and Chen, J. (2004). Aging properties of the residual life length of k-out-of-n systems with independent but non-identical components. Appl. Stoch. Models Business Industry 20, 143–153.CrossRefGoogle Scholar
Li, X. and Zhao, P. (2006). Some ageing properties of the residual life of k-out-of-n systems. IEEE Trans. Reliab. 55, 535–541.Google Scholar
Li, X. and Zhao, P. (2008). Stochastic comparison on general inactivity time and general residual life of k-out-of-n systems. Commun. Statist. Simul. Comput. 37, 1005–1019.Google Scholar
Li, X. and Zuo, M. J. (2002). On the behaviour of some new ageing properties based upon the residual life of k-out-of-n systems. J. Appl. Prob. 39, 426–433.Google Scholar
Lillo, R., Nanda, A. K. and Shaked, M. (2001). Preservation of some likelihood ratio orders by order statistics. Statist. Prob. Lett. 51, 111–119.CrossRefGoogle Scholar
Meilijson, I. (1981). Estimation of the lifetime distribution of the parts from autopsy statistics of the machine. J. Appl. Prob. 18, 829–838.Google Scholar
Müller, A. and Stoyan, D. (2002). Comparison Methods for Stochastic Models and Risks. John Wiley, New York.Google Scholar
Nanda, A. K. and Shaked, M. (2001). The hazard rate and the reversed hazard rate orders, with applications to order statistics. Ann. Inst. Statist. Math. 53, 853–864.CrossRefGoogle Scholar
Sadegh, M. K. (2008). Mean past and mean residual life functions of a parallel system with nonidentical components. Commun. Statist. Theory Meth. 37, 1134–1145.CrossRefGoogle Scholar
Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.Google Scholar
Xie, H. and Hu, T. (2008). Conditional ordering of generalized order statistics revisited. Prob. Eng. Inf. Sci. 22, 333–346.CrossRefGoogle Scholar
Xu, M. (2008). Ordering residual lifetimes of k-out-of-n systems with nonidentical components. Tech. Rep., Department of Mathematics and Statistics, Portland State University.Google Scholar