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TP2-Orderings and the IFR Property with Applications

Published online by Cambridge University Press:  27 July 2009

S. Durham ,
J. Lynch  and
W.J. Padgett
S. Durham
Affiliation:
Department of Statistics University of South Carolina, Columbia, South Carolina 29208
J. Lynch
Affiliation:
Department of Statistics University of South Carolina, Columbia, South Carolina 29208
W.J. Padgett
Affiliation:
Department of Statistics University of South Carolina, Columbia, South Carolina 29208
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Extract

In this paper, TP2 orderings of distributions and of survival functions are considered. It is shown that the first passage time of a Markov process with TP2- ordered transition distributions has an increasing failure rate (IFR). Conditions are also given for which mixtures of IFR distributions are IFR. A formula is obtained for the failure rate when the strength distribution is a function of both load and strength. This formula, in conjunction with the TP2-ordering on the strength survival functions and log-concavity of the strength and load variables, leads to an increasing failure rate for the strength distribution. Finally, two models based on this theory are presented which explain the IFR character of the strength distribution of fibrous composite materials.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 4 , Issue 1 , January 1990 , pp. 73 - 88
Copyright
Copyright © Cambridge University Press 1990

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