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On Two Damage Accumulation Models and Their Size Effects

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

F. Ballani ,
D. Stoyan  and
S. Wolf
F. Ballani*
Affiliation:
TU Bergakademie Freiberg
D. Stoyan*
Affiliation:
TU Bergakademie Freiberg
S. Wolf*
Affiliation:
TU Bergakademie Freiberg
*
∗ Postal address: Institute of Stochastics, TU Bergakademie Freiberg, Prüferstrasse 9, D-09596 Freiberg, Germany.
∗ Postal address: Institute of Stochastics, TU Bergakademie Freiberg, Prüferstrasse 9, D-09596 Freiberg, Germany.
∗ Postal address: Institute of Stochastics, TU Bergakademie Freiberg, Prüferstrasse 9, D-09596 Freiberg, Germany.
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Abstract

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Two cumulative damage models are considered, the inverse gamma process and a composed gamma process. They can be seen as ‘continuous’ analogues of Poisson and compound Poisson processes, respectively. For these models the first passage time distribution functions are derived. Inhomogeneous versions of these processes lead to models closely related to the Weibull failure model. All models show interesting size effects.

Keywords

Fracture theorydamage accumulationgamma processinverse gamma processWeibull distribution

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes 60K10: Applications (reliability, demand theory, etc.)
Secondary: 60G55: Point processes
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 1 , March 2007 , pp. 99 - 114
Copyright
Copyright © Applied Probability Trust 2007 

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