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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: [email protected]
Narayanaswamy Balakrishnan
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, CanadaL8S 4K1
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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

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