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Lifetime regression models based on a functional equation of physical nature

Published online by Cambridge University Press:  14 July 2016

Enrique Castillo  and
Janos Galambos
Enrique Castillo*
Affiliation:
University of Santander
Janos Galambos*
Affiliation:
Temple University
*
∗Postal address: Universidad de Santander, Escuela Tecnica Superior, Dpto. de Matematicas Aplicadas a la Ingenieria, Avda. da los Castros, s/n, Santander, Spain.
∗∗Postal address: Department of Mathematics, TU 038–16, Temple University, Philadelphia, PA 19122, USA.
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Abstract

There are a number of ad hoc regression models for the statistical analysis of lifetime data, but only a few examples exist in which physical considerations are used to characterize the model. In the present paper a complete characterization of a regression model is given by solving a functional equation recurring in the literature for the case of a fatigue problem. The result is that, if the lifetime for given values of the regressor variable and the regressor variable for a given lifetime are both Weibull variables (assumptions which are well founded, at least as approximations, from extreme-value theory in some concrete applications), there are only three families of (conditional) distribution for the lifetime (or for the regressor variable). This model is then applied to a practical problem for illustration.

Keywords

RANDOM LIFEFATIGUE FAILURESTRESSCHARACTERIZATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 160 - 169
Copyright
Copyright © Applied Probability Trust 1987 

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References

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