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Effective procedure of verifying stochastic ordering of system lifetimes

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

Published online by Cambridge University Press:  16 January 2019

Tomasz Rychlik ,
Jorge Navarro  and
Rafael Rubio
Tomasz Rychlik*
Affiliation:
Polish Academy of Sciences
Jorge Navarro*
Affiliation:
Universidad de Murcia
Rafael Rubio*
Affiliation:
Universidad de Murcia
*
* Postal address: Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00656 Warsaw, Poland. Email address: trychlik@impan.pl
** Postal address: Facultad de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain.
** Postal address: Facultad de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain.
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Abstract

The Samaniego signature is a relevant tool for studying the performance of a system whose component lifetimes are exchangeable. It is well known that the stochastic ordering of the signatures of two systems implies the same for the respective system lifetimes. We prove that the reverse claim is not true when the component lifetimes are independent and identically distributed. There exist small proportions of systems with stochastically ordered lifetimes whose signatures are not ordered. We present a simple procedure in order to check whether the system lifetimes are stochastically ordered even if their signatures are not comparable.

Keywords

Coherent systemmixed systemSamaniego signaturestochastic order

MSC classification

Primary: 60E15: Inequalities; stochastic orderings 62N05: Reliability and life testing
Secondary: 62G30: Order statistics; empirical distribution functions
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 4 , December 2018 , pp. 1261 - 1271
Copyright
Copyright © Applied Probability Trust 2018 

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References

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