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SOME NEW RELIABILITY BOUNDS FOR SUMS OF NBUE RANDOM VARIABLES

Published online by Cambridge University Press:  02 November 2010

Steven G. From
Steven G. From
Affiliation:
Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182–0243 E-mail: [email protected]
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Abstract

In this article, we discuss some new upper and lower bounds for the survivor function of the sum of n independent random variables each of which has an NBUE (new better than used in expectation) distribution. In some cases, only the means of the random variables are assumed known. These bounds are compared to the sharp bounds given in Cheng and Lam [6], which requires both means and variances known. Although the new bounds are not sharp, they often produce better upper bounds for the survivor function in the extreme right tail of many NBUE lifetime distributions, an important special case in applications. Moreover, a lower bound exists in one case not handled by the lower bounds of Theorem 3 in Cheng and Lam [6]. Numerical studies are presented along with theoretical discussions.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 1 , January 2011 , pp. 83 - 102
Copyright
Copyright © Cambridge University Press 2011

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