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ROLE OF EQUILIBRIUM DISTRIBUTION IN RELIABILITY STUDIES

Published online by Cambridge University Press:  27 February 2007

Ramesh C. Gupta
Ramesh C. Gupta
Affiliation:
Department of Mathematics and Statistics, University of Maine, Orono, ME 04469-5752, E-mail: ramesh_gupta@umit.maine.edu
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Abstract

The equilibrium distribution arises as the limiting distribution of the forward recurrence time in a renewal process. The purpose of this article is to study the relationships between the equilibrium distributions (including its higher derivates) and the original distributions. Some stochastic order relations and the relations between their aging properties are investigated and some applications in the field of insurance and financial investments are given. In addition, the relation between the equilibrium distribution of a series system and the series system of equilibrium distribution is investigated. Bivariate equilibrium distribution whose reliability properties are consistent with those of the univariate equilibrium distribution is defined.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 2 , April 2007 , pp. 315 - 334
Copyright
© 2007 Cambridge University Press

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