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Continuous Mixtures with Bathtub-Shaped Failure Rates

Part of: Survival analysis and censored data Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Henry W. Block ,
Yulin Li ,
Thomas H. Savits  and
Jie Wang
Henry W. Block*
Affiliation:
University of Pittsburgh
Yulin Li*
Affiliation:
The University of Toledo
Thomas H. Savits*
Affiliation:
University of Pittsburgh
Jie Wang*
Affiliation:
University of Pittsburgh
*
∗Postal address: Department of Statistics, University of Pittsburgh, 2717 Cathedral of Learning, Pittsburgh, PA 15260, USA.
∗∗∗∗Postal address: Department of Statistics, University of Pittsburgh, 2717 Cathedral of Learning, Pittsburgh, PA 15260, USA.
∗Postal address: Department of Statistics, University of Pittsburgh, 2717 Cathedral of Learning, Pittsburgh, PA 15260, USA.
∗Postal address: Department of Statistics, University of Pittsburgh, 2717 Cathedral of Learning, Pittsburgh, PA 15260, USA.
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Abstract

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The failure rate of a mixture of even the most standard distributions used in reliability can have a complicated shape. However, failure rates of mixtures of two carefully selected distributions will have the well-known bathtub shape. Here we show that mixtures of whole families of distribtions can have a bathtub-shaped failure rate.

Keywords

Reliabilitybathtub-shaped failure rate

MSC classification

Secondary: 62N05: Reliability and life testing 90B25: Reliability, availability, maintenance, inspection
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 1 , March 2008 , pp. 260 - 270
Copyright
Copyright © Applied Probability Trust 2008 

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