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Preservation of generalized bathtub-shaped functions

Part of: Survival analysis and censored data Special processes

Published online by Cambridge University Press:  14 July 2016

Thomas H. Savits
Thomas H. Savits*
Affiliation:
University of Pittsburgh
*
∗ Postal address: Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA. Email address: ths@stat.pitt.edu
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Abstract

Block, Savits and Singh previously presented a preservation result for bathtub-shaped functions. In this paper, we strengthen and extend their results to a class of functions which allow for more than one change of monotonicity. Various applications are also considered.

Keywords

Bathtub-shaped functionpreservationIFRDFRreliabilityorderings

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 2 , June 2003 , pp. 473 - 484
Copyright
Copyright © Applied Probability Trust 2003 

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Footnotes

Supported by NSF Grant DMS-0072207.

References

Barlow, R. E., and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.Google Scholar
Billingsley, P. (1995). Probability and Measure, 3rd edn. John Wiley, New York.Google Scholar
Block, H. W., Jong, Y.-K., and Savits, T. H. (1999). Bathtub functions and burn-in. Prob. Eng. Inf. Sci. 13, 497–507.Google Scholar
Block, H. W., Savits, T. H., and Singh, H. (2002). A criterion for burn-in which balances mean residual life and residual variance. Operat. Res. 50, 290–296.Google Scholar
Glaser, R. E. (1980). Bathtub and related failure rate characterizations. J. Amer. Statist. Assoc. 75, 667–672.CrossRefGoogle Scholar
Leemis, L. M. (1995). Reliability: Probability Models and Statistical Methods. Prentice-Hall, Englewood Cliffs, New Jersey.Google Scholar
Metzger, C. and Rüschendorf, L. (1991). Conditional variability ordering of distributions. Ann. Operat. Res. 32, 127–140.CrossRefGoogle Scholar
Shaked, M., and Shanthikumar, J. G. (1994). Stochastic Orders and Their Applications. Academic Press, San Diego, CA.Google Scholar