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Effective procedure of verifying stochastic ordering of system lifetimes

  • Tomasz Rychlik (a1), Jorge Navarro (a2) and Rafael Rubio (a2)


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.


Corresponding author

* Postal address: Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00656 Warsaw, Poland. Email address:
** Postal address: Facultad de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain.
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MSC classification

Effective procedure of verifying stochastic ordering of system lifetimes

  • Tomasz Rychlik (a1), Jorge Navarro (a2) and Rafael Rubio (a2)


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