Lifetime Data Analysis

, Volume 10, Issue 3, pp 213–227

Covariates and Random Effects in a Gamma Process Model with Application to Degradation and Failure

  • Jerry Lawless
  • Martin Crowder


The gamma process is a natural model for degradation processes in which deterioration is supposed to take place gradually over time in a sequence of tiny increments. When units or individuals are observed over time it is often apparent that they degrade at different rates, even though no differences in treatment or environment are present. Thus, in applying gamma-process models to such data, it is necessary to allow for such unexplained differences. In the present paper this is accomplished by constructing a tractable gamma-process model incorporating a random effect. The model is fitted to some data on crack growth and corresponding goodness-of-fit tests are carried out. Prediction calculations for failure times defined in terms of degradation level passages are developed and illustrated.

degradation frailty gamma process random effects reliability repeated measures wear 


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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Jerry Lawless
    • 1
  • Martin Crowder
    • 2
  1. 1.Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Department of MathematicsImperial CollegeLondonUK

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