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A Note on the Failure Rates in Finite Mixed Populations

Part of: Distribution theory - Probability Operations research and management science

Published online by Cambridge University Press:  04 February 2016

Ji Hwan Cha  and
Massimiliano Giorgio
Ji Hwan Cha*
Affiliation:
Ewha Womans University
Massimiliano Giorgio*
Affiliation:
Second University of Naples
*
∗ Postal address: Department of Statistics, Ewha Womans University, Seoul, 120-750, Korea. Email address: jhcha@ewha.ac.kr
∗∗ Postal address: Department of Aerospace and Mechanical Engineering, Second University of Naples, 81031 Aversa (CE), Italy. Email address: massimiliano.giorgio@unina2.it
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Abstract

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Almost all populations existing in the real world are finite populations. Specifically, in the areas relevant to lifetime modeling and analysis, finite populations are frequently encountered. However, descriptions of failure/survival patterns of elements in the finite population have not yet been properly established. In particular, it is questionable whether the ordinary failure rate can be defined for finite populations in the same way and whether the corresponding interpretations are still valid. In this paper we consider two kinds of finite mixed population and provide new definitions for their failure rates. Then we clarify the notion of failure rate in finite populations.

Keywords

Failure rateproportion-based failure rateheterogeneous populationfinite mixed population

MSC classification

Primary: 60E05: Distributions
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 405 - 415
Copyright
© Applied Probability Trust 

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