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

Author

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  • Marco Burkschat

    (RWTH Aachen University)

  • Tomasz Rychlik

    (Polish Academy of Sciences)

Abstract

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.

Suggested Citation

  • Marco Burkschat & Tomasz Rychlik, 2018. "Sharp inequalities for quantiles of system lifetime distributions from failure-dependent proportional hazard model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 618-638, September.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:3:d:10.1007_s11749-017-0564-0
    DOI: 10.1007/s11749-017-0564-0
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    References listed on IDEAS

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