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Ageing and stochastic comparisons for a covariate failure model

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Franco Pellerey  and
Patrizia Semeraro
Franco Pellerey*
Affiliation:
Politecnico di Torino
Patrizia Semeraro*
Affiliation:
Università di Torino
*
∗ Postal address: Dipartimento di Matematica, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy. Email address: pellerey@calvino.polito.it
∗∗ Postal address: Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy.
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Abstract

Ebrahimi (2001) proposes an interesting model for assessing a system's reliability, expressing the failure time of the system in terms of a deterioration process and covariates. He also provides illustrative examples and gives some properties of the model. In this note, we give conditions for negative ageing of the system's lifetime, and we correct one of his statements. Moreover, for the lifetimes of two systems of the same kind, some stochastic comparisons are presented.

Keywords

System reliabilityNWUNWUEDFRDFRAusual stochastic orderincreasing convex orderincreasing concave order

MSC classification

Primary: 60E05: Distributions 60E15: Inequalities; stochastic orderings
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 421 - 425
Copyright
Copyright © Applied Probability Trust 2002 

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References

[1] Barlow, R. E., and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.Google Scholar
[2] Ebrahimi, N. (2001). A stochastic covariate failure model for assessing system reliability. J. Appl. Prob. 38, 761–767.Google Scholar
[3] Lindqvist, B. H. (1988). Association of probability measures on partially ordered spaces. J. Multivariate Anal. 26, 111–132.Google Scholar
[4] Shaked, M., and Shanthikumar, J. G. (1994). Stochastic Orders and Their Applications. Academic Press, San Diego, CA.Google Scholar