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Bounds on Variances of Lifetimes of Coherent and Mixed Systems

Part of: Distribution theory - Probability Nonparametric inference Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

Krzysztof Jasiński ,
Jorge Navarro  and
Tomasz Rychlik
Krzysztof Jasiński*
Affiliation:
Nicolaus Copernicus University
Jorge Navarro*
Affiliation:
Universidad de Murcia
Tomasz Rychlik*
Affiliation:
Nicolaus Copernicus University and Polish Academy of Sciences
*
∗Postal address: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12, 87100 Toruń, Poland. Email address: [email protected]
∗∗Postal address: Facultad de Matematicas, Universidad de Murcia, 30100 Murcia, Spain. Email address: [email protected]
∗∗∗Postal address: Institute of Mathematics, Polish Academy of Sciences, Chopina 12, 87100 Toruń, Poland. Email address: [email protected]
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Abstract

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We consider coherent and mixed reliability systems composed of elements with independent and identically distributed lifetimes. We present upper bounds on variances of system lifetimes, expressed in terms of variances of single components. We also discuss attainability conditions and some special cases and examples.

Keywords

Coherent systemmixed systemvarianceSamaniego signatureupper bound

MSC classification

Secondary: 62N05: Reliability and life testing 60E15: Inequalities; stochastic orderings 62G30: Order statistics; empirical distribution functions
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 3 , September 2009 , pp. 894 - 908
Copyright
Copyright © Applied Probability Trust 2009 

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