, Volume 27, Issue 3, pp 618–638 | Cite as

Sharp inequalities for quantiles of system lifetime distributions from failure-dependent proportional hazard model

  • Marco BurkschatEmail author
  • Tomasz Rychlik
Original Paper


We consider coherent systems with components whose exchangeable lifetime distributions come from the failure-dependent proportional hazard model, i.e., the consecutive failures satisfy the assumptions of the generalized order statistics model. For a fixed system and given failure rate proportion jumps, we provide sharp bounds on the deviations of system lifetime distribution quantiles from the respective quantiles of single component nominal and actual lifetime distributions. The bounds are expressed in the scale units generated by the absolute moments of various orders of the component lifetime centered about the median of its distribution.


Coherent system Generalized order statistics Samaniego signature Quantile Sharp bound 

Mathematics Subject Classification

Primary 62N05 Secondary 60E15 62G30 



The second author was supported by National Science Centre, Poland, Grant No. 2015/19/B/ST1/03100. The authors thank the anonymous referees and associate editor for valuable comments that allowed them to improve the presentation of the results.


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2017

Authors and Affiliations

  1. 1.RWTH Aachen UniversityAachenGermany
  2. 2.Institute of MathematicsPolish Academy of SciencesWarsawPoland

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