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On unimodality of the lifetime distribution of coherent systems with failure-dependent component lifetimes

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

Published online by Cambridge University Press:  26 July 2018

M. Bieniek  and
M. Burkschat
M. Bieniek*
Affiliation:
Maria Curie Skłodowska University
M. Burkschat*
Affiliation:
RWTH Aachen University
*
* Postal address: Institute of Mathematics, Maria Curie Skłodowska University, Pl. Marii Curie Skłodowskiej 1, 20-031 Lublin, Poland. Email address: mariusz.bieniek@umcs.lublin.pl
** Postal address: Institute of Statistics, RWTH Aachen University, D-52056 Aachen, Germany. Email address: marco.burkschat@rwth-aachen.de
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Abstract

We study the conditions for unimodality of the lifetime distribution of a coherent system when the ordered component lifetimes in the system are described by generalized order statistics. Results for systems with independent and identically distributed lifetimes of components are included in this setting. The findings are illustrated with some examples for different types of systems. In particular, coherent systems with strictly bimodal density functions are presented in the case of independent standard uniform distributed lifetimes of components. Furthermore, we use the results to derive a sharp upper bound on the expected system lifetime in terms of the mean and the standard deviation of the underlying distribution.

Keywords

Unimodalitybimodalitysignaturecoherent systemsequential order statisticsgeneralized order statisticsvariation diminishing propertybounds

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 60E05: Distributions 60E15: Inequalities; stochastic orderings
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 2 , June 2018 , pp. 473 - 487
Copyright
Copyright © Applied Probability Trust 2018 

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