The identifiability problem for generalised competing risk models with non-symmetric virtual ages

M.R. Burnham, T.J. Bedford, L.A. Walls

Research output: Contribution to conference › Paper

Abstract

The identifiability problem is well-known in competing risks (1). Recently a generalised competing risks framework was proposed by Doyen and Gaudoin(2), along with several subclasses of this framework which incorporate virtual age models(3). The identifiability problem is still present in generalised competing risk models with symmetrical virtual ages for each of the risks, however it is unclear to what extent this is true for generalised competing risk models with non-symmetrical virtual ages for the risks. Bedford and Lindqvist(4) have constructed an example of a two component system in which, every time a component fails it is restored to a state "as good as new", while the remaining components are restored to a state "as bad as old". In this example they prove that the model can be uniquely identified. Doyen and Gaudoin(2) show that this example is a particular instance of a generalised competing risks model with non-symmetrical virtual ages. In this paper we generalise the Bedford and Lindqvist example to show identifiability of systems with n components. We also discuss how this proof has been constructed to more easily allow for the consideration of other virtual age models in future work.
LanguageEnglish
Publication statusUnpublished - Jun 2009
EventMathematical Methods in Reliability - Moscow, Russia
Duration: 22 Jun 2009 → 27 Jun 2009

Conference

ConferenceMathematical Methods in Reliability
CityMoscow, Russia
Period22/06/09 → 27/06/09

Keywords

  • identifiability
  • competing risks
  • risks framework
  • virtual age models
  • non-symmetrical virtual ages

Cite this

Burnham, M. R., Bedford, T. J., & Walls, L. A. (2009). The identifiability problem for generalised competing risk models with non-symmetric virtual ages. Paper presented at Mathematical Methods in Reliability, Moscow, Russia, .
Burnham, M.R. ; Bedford, T.J. ; Walls, L.A. / The identifiability problem for generalised competing risk models with non-symmetric virtual ages. Paper presented at Mathematical Methods in Reliability, Moscow, Russia, .
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Burnham, MR, Bedford, TJ & Walls, LA 2009, 'The identifiability problem for generalised competing risk models with non-symmetric virtual ages' Paper presented at Mathematical Methods in Reliability, Moscow, Russia, 22/06/09 - 27/06/09, .

The identifiability problem for generalised competing risk models with non-symmetric virtual ages. / Burnham, M.R.; Bedford, T.J.; Walls, L.A.

2009. Paper presented at Mathematical Methods in Reliability, Moscow, Russia, .

Research output: Contribution to conference › Paper

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AU - Walls, L.A.

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AB - The identifiability problem is well-known in competing risks (1). Recently a generalised competing risks framework was proposed by Doyen and Gaudoin(2), along with several subclasses of this framework which incorporate virtual age models(3). The identifiability problem is still present in generalised competing risk models with symmetrical virtual ages for each of the risks, however it is unclear to what extent this is true for generalised competing risk models with non-symmetrical virtual ages for the risks. Bedford and Lindqvist(4) have constructed an example of a two component system in which, every time a component fails it is restored to a state "as good as new", while the remaining components are restored to a state "as bad as old". In this example they prove that the model can be uniquely identified. Doyen and Gaudoin(2) show that this example is a particular instance of a generalised competing risks model with non-symmetrical virtual ages. In this paper we generalise the Bedford and Lindqvist example to show identifiability of systems with n components. We also discuss how this proof has been constructed to more easily allow for the consideration of other virtual age models in future work.

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Burnham MR, Bedford TJ, Walls LA. The identifiability problem for generalised competing risk models with non-symmetric virtual ages. 2009. Paper presented at Mathematical Methods in Reliability, Moscow, Russia, .

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