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

Marco Burkschat () and Tomasz Rychlik
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Marco Burkschat: RWTH Aachen University
Tomasz Rychlik: Polish Academy of Sciences

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2018, vol. 27, issue 3, No 8, 618-638

Abstract: 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.

Keywords: Coherent system; Generalized order statistics; Samaniego signature; Quantile; Sharp bound; Primary 62N05; Secondary 60E15; 62G30 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11749-017-0564-0

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