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On the collapsibility of lifetime regression models

Part of: Operations research and management science Special processes Survival analysis and censored data

Published online by Cambridge University Press:  01 July 2016

Thierry Duchesne  and
Jeffrey S. Rosenthal
Thierry Duchesne*
Affiliation:
Université Laval, Québec
Jeffrey S. Rosenthal*
Affiliation:
University of Toronto
*
∗ Postal address: Département de Mathématiques et de Statistique, Pavillon Alexandre-Vachon, Université Laval, Québec, Québec G1K 7P4, Canada. Email address: duchesne@mat.ulaval.ca
∗∗ Postal address: Department of Statistics, University of Toronto, 100 St. George Street, Toronto, Ontario M5S 3G3, Canada.
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Abstract

In this paper we derive conditions on the internal wear process under which the resulting time to failure model will be of the simple collapsible form when the usage accumulation history is available. We suppose that failure occurs when internal wear crosses a certain threshold or a traumatic event causes the item to fail. We model the infinitesimal increment in internal wear as a function of time, accumulated internal wear, and usage history, and we derive conditions on this function to get a collapsible model for the distribution of time to failure given the usage history. We reach the conclusion that collapsible models form the subset of accelerated failure time models with time-varying covariates for which the time transformation function satisfies certain simple properties.

Keywords

Accelerated failure time modeladditive hazard modelcollapsible modeldegradationdifferential equationdiffusiongamma processinternal weartraumatic eventusage rate

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62N05: Reliability and life testing 90B25: Reliability, availability, maintenance, inspection
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 35 , Issue 3 , September 2003 , pp. 755 - 772
Copyright
Copyright © Applied Probability Trust 2003 

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