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The limiting failure rate for a convolution of life distributions

Part of: Special processes Survival analysis and censored data

Published online by Cambridge University Press:  30 March 2016

Henry W. Block ,
Naftali A. Langberg  and
Thomas H. Savits
Henry W. Block*
Affiliation:
University of Pittsburgh
Naftali A. Langberg*
Affiliation:
Haifa University
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.
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Abstract

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In this paper we investigate the limiting behavior of the failure rate for the convolution of two or more life distributions. In a previous paper on mixtures, Block, Mi and Savits (1993) showed that the failure rate behaves like the limiting behavior of the strongest component. We show a similar result here for convolutions. We also show by example that unlike a mixture population, the ultimate direction of monotonicity does not necessarily follow that of the strongest component.

Keywords

Reliabilityfailure rate functionincreasing failure ratedecreasing failure rateconvolution

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 60K10: Applications (reliability, demand theory, etc.)

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 52 , Issue 3 , September 2015 , pp. 894 - 898
Copyright
Copyright © 2015 by the Applied Probability Trust 

References

Block, H. and Joe, H. (1997). Tail behavior of the failure rate functions of mixtures. Lifetime Data Anal. 3, 269–288.CrossRefGoogle ScholarPubMed
Block, H. W., Langberg, N. A. and Savits, T. H. (2014). The limiting failure rate for a convolution of gamma distributions. Prob. Statist. Lett. 94, 176–180 CrossRefGoogle Scholar
Block, H. W., Li, Y. and Savits, T. H. (2003). Initial and final behaviour of failure rate functions for mixtures and systems. J. Appl. Prob. 40, 721–740.CrossRefGoogle Scholar
Block, H. W., Mi, J. and Savits, T. H. (1993). Burn-in and mixed populations. J. Appl. Prob. 30, 692–702.CrossRefGoogle Scholar
Lai, C.-D. and Xie, M. (2006). Stochastic Ageing and Dependence for Reliability. Springer, New York.Google Scholar
Marshall, A. W. and Olkin, I. (2007). Life Distributions. Springer, New York.Google Scholar
Navarro, J. and Hernandez, P. J. (2004). How to obtain bathtub-shaped failure rate models from normal mixtures. Prob. Eng. Inf. Sci. 18, 511–531.CrossRefGoogle Scholar
Navarro, J., Guillamon, A. and Ruiz, M. C. (2009). Generalized mixtures in reliability modelling: applications to the construction of bahtub shaped hazard models and the study of systems. Appl. Stoch. Models Business Industry. 25, 323–337.CrossRefGoogle Scholar
Wondmagegnehu, E. T., Navarro, J. and Hernandez, P. J. (2005). Bathtub shaped failure rates from mixtures: a practical point of view. IEEE Trans. Reliab. 54, 270–275.CrossRefGoogle Scholar