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Failure models indexed by two scales

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

Published online by Cambridge University Press:  01 July 2016

Nozer D. Singpurwalla  and
Simon P. Wilson
Nozer D. Singpurwalla*
Affiliation:
The George Washington University
Simon P. Wilson*
Affiliation:
Trinity College, Dublin
*
∗ Postal address: Department of Operations Research, The George Washington University, Washington, DC 20052, USA. Email address: [email protected]
∗∗ Postal address: School of Systems and Data Studies, Trinity College, Dublin 2, Ireland.
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Abstract

Much of the literature in reliability and survival analysis considers failure models indexed by a single scale. There are situations which require that failure be described by several scales. An example from reliability is items under warranty whose failure is recorded by time and amount of use. An example from survival analysis is the death of a mine worker which is noted by age and the duration of exposure to dust.

This paper proposes an approach for developing probabilistic models indexed by two scales: time, and usage, a quantity that is related to time. The relationship between the scales is described by an additive hazards model. The evolution of usage is described by stochastic processes like the Poisson, the gamma and the Markov additive. The paper concludes with an application involving the setting of warranties. Two features differentiate this work from related efforts: a use of specific processes for describing usage, and a use of Monte Carlo techniques for generating the models.

Keywords

Additive hazardbiometrygamma processMarkov additive processPoisson processreliabilitysimulationsurvival analysiswarranties

MSC classification

Primary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) 62N05: Reliability and life testing 90B25: Reliability, availability, maintenance, inspection
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 4 , December 1998 , pp. 1058 - 1072
Copyright
Copyright © Applied Probability Trust 1998 

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