Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-09T01:35:50.020Z Has data issue: false hasContentIssue false
  • English
  • Français

Initial and final behaviour of failure rate functions for mixtures and systems

Part of: Survival analysis and censored data Distribution theory

Published online by Cambridge University Press:  14 July 2016

Henry W. Block ,
Yulin Li  and
Thomas H. Savits
Henry W. Block*
Affiliation:
University of Pittsburgh
Yulin Li*
Affiliation:
University of Pittsburgh
Thomas H. Savits*
Affiliation:
University of Pittsburgh
*
∗Postal address: Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA
∗Postal address: Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA
∗Postal address: Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

MixtureIFRDFRbathtub shapefailure rateasymptotic behaviourinitial behaviourcoherent system

MSC classification

Primary: 62E10: Characterization and structure theory
Secondary: 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 721 - 740
Copyright
Copyright © Applied Probability Trust 2003 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The first and third authors were supported by NSF grant DMS-0072207.

References

Barlow, R. E., and Proschan, F. (1975). Statistical Theory of Reliability. Holt, Rinehart and Winston, New York.Google Scholar
Barlow, R. E., Marshall, A. M., and Proschan, F. (1963). Properties of probability distributions with monotone hazard rate. Ann. Math. Statist. 34, 375–389.CrossRefGoogle Scholar
Block, H. W., and Joe, H. (1997). Tail behavior of the failure rate functions of mixtures. Lifetime Data Anal. 3, 269–288.Google Scholar
Block, H. W., and Savits, T. H. (1997). Burn-in. Statist. Sci. 12, 1–19.Google Scholar
Block, H. W., Mi, J., and Savits, T. H. (1993). Burn-in and mixed populations. J. Appl. Prob. 30, 692–702.Google Scholar
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.CrossRefGoogle Scholar
Clarotti, C. A., and Spizzichino, F. (1990). Bayes burn-in decision procedures. Prob. Eng. Inf. Sci. 4, 437–445.Google Scholar
Gupta, P. L., and Gupta, R. C. (1996). Ageing characteristics of the Weibull mixtures. Prob. Eng. Inf. Sci. 10, 591–600.Google Scholar
Gurland, J., and Sethuraman, J. (1995). How pooling failure data may reverse increasing failure rates. J. Amer. Statist. Assoc. 90, 1416–1423.CrossRefGoogle Scholar