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Extreme Dispersions of Semicoherent and Mixed System Lifetimes

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

Published online by Cambridge University Press:  30 January 2018

Patryk Miziuła  and
Tomasz Rychlik
Patryk Miziuła*
Affiliation:
Nicolaus Copernicus University
Tomasz Rychlik*
Affiliation:
Polish Academy of Sciences
*
∗ Postal address: Faculty of Mathematics and Computer Sciences, Nicolaus Copernicus University, Chopina 12, 87-100 Torun, Poland.
∗∗ Postal address: Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warsaw, Poland. Email address: trychlik@impan.pl
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Abstract

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We consider semicoherent and mixed systems with exchangeable components. We present sharp lower and upper bounds on various dispersion measures (in particular, variance and median absolute deviation) of the system lifetime, expressed in terms of the system signature and the dispersion of a single component lifetime. We construct joint exchangeable distributions of component lifetimes with two-point marginals which attain the bounds in the limit.

Keywords

Semicoherent systemmixed systemSamaniego signatureexchangeable random variablessharp bounddispersion measurevariancemedian absolute deviation

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 60E15: Inequalities; stochastic orderings 62G30: Order statistics; empirical distribution functions
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 1 , March 2015 , pp. 117 - 128
Copyright
© Applied Probability Trust 

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