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ALTERNATIVE ANALYSIS OF FINITE-TIME PROBABILITY DISTRIBUTIONS OF RENEWAL THEORY

Published online by Cambridge University Press:  02 January 2014

Percy H. Brill
Percy H. Brill*
Affiliation:
Department of Mathematics and Statistics and Department of Management Science, University of Windsor, Canada. E-mail: brill@uwindsor.ca
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Abstract

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We introduce a level-crossing analysis of the finite time-t probability distributions of the excess life, age, total life, and related quantities of renewal processes. The technique embeds the renewal process as one cycle of a regenerative process with a barrier at level t, whose limiting probability density function leads directly to the time-t quantities. The new method connects the analysis of renewal processes with the analysis of a large class of stochastic models of Operations Research. Examples are given.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 2 , April 2014 , pp. 183 - 201
Copyright
Copyright © Cambridge University Press 2014 

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