Initial and final behaviour of failure rate functions for mixtures and systems
Henry W. Block, Yulin Li, and Thomas H. Savits
Source: J. Appl. Probab.
Volume 40, Number 3
In this paper we consider the initial and asymptotic behaviour of
the failure rate function resulting from mixtures of
subpopulations and formation of coherent systems. In particular,
it is shown that the failure rate of a mixture has the same
limiting behaviour as the failure rate of the strongest
subpopulation. A similar result holds for systems except the role
of strongest subpopulation is replaced by strongest min path set.
Full-text: Access denied (no subscription
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1059060898
Digital Object Identifier: doi:10.1239/jap/1059060898
Mathematical Reviews number (MathSciNet): MR1993263
Zentralblatt MATH identifier: 02066247
Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability. Holt, Rinehart and Winston, New York.
Mathematical Reviews (MathSciNet): MR438625
Barlow, R. E., Marshall, A. M. and Proschan, F. (1963). Properties of probability distributions with monotone hazard rate. Ann. Math. Statist. 34, 375--389.
Mathematical Reviews (MathSciNet): MR171328
Block, H. W. and Joe, H. (1997). Tail behavior of the failure rate functions of mixtures. Lifetime Data Anal. 3, 269--288.
Block, H. W. and Savits, T. H. (1997). Burn-in. Statist. Sci. 12, 1--19.
Block, H. W., Mi, J. and Savits, T. H. (1993). Burn-in and mixed populations. J. Appl. Prob. 30, 692--702.
Block, H. W., Savits, T. H. and Wondmagegnehu, E. T. (2003). Mixtures of distributions with increasing linear failure rates. J. Appl. Prob. 40, 485--504.
Clarotti, C. A. and Spizzichino, F. (1990). Bayes burn-in decision procedures. Prob. Eng. Inf. Sci. 4, 437--445.
Gupta, P. L. and Gupta, R. C. (1996). Ageing characteristics of the Weibull mixtures. Prob. Eng. Inf. Sci. 10, 591--600.
Gurland, J. and Sethuraman, J. (1995). How pooling failure data may reverse increasing failure rates. J. Amer. Statist. Assoc. 90, 1416--1423.