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CHARACTERIZATIONS OF THE RHR AND MIT ORDERINGS AND THE DRHR AND IMIT CLASSES OF LIFE DISTRIBUTIONS

Published online by Cambridge University Press:  31 August 2005

I. A. Ahmad  and
M. Kayid
I. A. Ahmad
Affiliation:
Department of Statistics and Actuarial Science, University of Central Florida, Orlando, Florida 32816-2370, E-mail: iahmad@mail.ucf.edu
M. Kayid
Affiliation:
Department of Mathematics, Faculty of Education (Suez), Suez Canal University, Suez, Egypt, E-mail: drkayid@yahoo.com
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Abstract

Two well-known orders that have been introduced and studied in reliability theory are defined via stochastic comparison of inactivity time: the reversed hazard rate order and the mean inactivity time order. In this article, some characterization results of those orders are given. We prove that, under suitable conditions, the reversed hazard rate order is equivalent to the mean inactivity time order. We also provide new characterizations of the decreasing reversed hazard rate (increasing mean inactivity time) classes based on variability orderings of the inactivity time of k-out-of-n system given that the time of the (n − k + 1)st failure occurs at or sometimes before time t ≥ 0. Similar conclusions based on the inactivity time of the component that fails first are presented as well. Finally, some useful inequalities and relations for weighted distributions related to reversed hazard rate (mean inactivity time) functions are obtained.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 19 , Issue 4 , October 2005 , pp. 447 - 461
Copyright
© 2005 Cambridge University Press

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