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Characterizations of classes of lifetime distributions generalizing the NBUE class

Published online by Cambridge University Press:  14 July 2016

Bernhard Klar*
Affiliation:
Universität Karlsruhe
Alfred Müller*
Affiliation:
Universität Karlsruhe
*
Postal address: Institut für Mathematische Stochastik, Universität Karlsruhe, Kaiserstr. 12, D-76128 Karlsruhe, Germany. Email address: [email protected]
∗∗ Postal address: Institut für Wirtschaftstheorie und Operations Research, Universität Karlsruhe, Kaiserstr. 12, D-76128 Karlsruhe, Germany.

Abstract

We introduce a new class of lifetime distributions exhibiting a notion of positive ageing, called the ℳ-class, which is strongly related to the well-known ℒ-class. It is shown that distributions in the ℳ-class cannot have an undesirable property recently observed in an example of an ℒ-class distribution by Klar (2002). Moreover, it is shown how these and related classes of life distributions can be characterized by expected remaining lifetimes after a family of random times, thus extending the notion of NBUE. We give examples of ℳ-class distributions by using simple sufficient conditions, and we derive reliability bounds for distributions in this class.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2003 

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