Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-13T06:52:45.485Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochastic comparison of parallel systems with heterogeneous exponential components

Part of: Distribution theory - Probability Operations research and management science

Published online by Cambridge University Press:  15 September 2017

Bin Cheng  and
Jiantian Wang
Bin Cheng*
Affiliation:
Columbia University
Jiantian Wang*
Affiliation:
Kean University
*
* Postal address: Department of Biostatistics, Mailman School of Public Health, Columbia University, 722 West 168th Street, New York, NY 10032, USA. Email address: [email protected]
** Postal address: School of Mathematical Sciences, Kean University, Union, NJ 07083, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we provide a sufficient condition for mean residual life ordering of parallel systems with n ≥ 3 heterogeneous exponential components.

Keywords

Mean residual life orderreciprocal majorizationparallel systemorder statisticsproportional hazard model

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60E15: Inequalities; stochastic orderings
Type
Short Communications
Information
Journal of Applied Probability , Volume 54 , Issue 3 , September 2017 , pp. 970 - 976
Copyright
Copyright © Applied Probability Trust 2017 

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] Balakrishnan, N. and Zhao, P. (2013). Ordering properties of order statistics from heterogeneous populations: a review with an emphasis on some recent developments. Prob. Eng. Inf. Sci. 27, 403–443. CrossRefGoogle Scholar
[2] Dykstra, R., Kochar, S. and Rojo, J. (1997). Stochastic comparisons of parallel systems of heterogeneous exponential components. J. Statist. Planning Infer. 65, 203–211. CrossRefGoogle Scholar
[3] Joo, S. and Mi, J. (2010). Some properties of hazard rate functions of systems with two components. J. Statist. Planning Infer. 140, 444–453. CrossRefGoogle Scholar
[4] Misra, N. and Misra, A. K. (2013). On comparison of reversed hazard rates of two parallel systems comprising of independent gamma components. Statist. Prob. Lett. 83, 1567–1570. CrossRefGoogle Scholar
[5] Pledger, G. and Proschan, F. (1971). Comparison of order statistics and of spacings from heterogeneous distributions. In Optimizing Methods in Statistics, Academic Press, New York, pp. 89–113. Google Scholar
[6] Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York. Google Scholar
[7] Torrado, N. and Kochar, S. C. (2015). Stochastic order relations among parallel systems from Weibull distributions. J. Appl. Prob. 52, 102–116. Google Scholar
[8] Zhao, P. and Balakrishnan, N. (2011). MRL ordering of parallel systems with two heterogeneous components. J. Statist. Planning Infer. 141, 631–638. Google Scholar
[9] Zhao, P. and Balakrishnan, N. (2011). Some characterization results for parallel systems with two heterogeneous exponential components. Statistics 45, 593–604. CrossRefGoogle Scholar