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Bayesian models for a change-point in failure rate
Abstract
The failure rate function r(x) provides a way to study the aging of a unit in a reliability study or in the analysis of survival data. A change in trend in the aging of the unit may be modelled by a change-point, call it $\theta$, in the failure rate. Such a model can be expressed by writing$$r(x) = \left\cases{a(x)\ 0\le x\le\theta\cr\cr b(x)\ x > \theta.\cr}$$For example, components may go through a "burn-in" phase in which the failure rate is high, after which the failure rate levels off at a lower rate. Estimation of the change-point may be of interest in certain situations. In the example mentioned above, a manufacturer may want to sell only those components which have survived the burn-in phase, that is, have survived to time $\theta$. We consider a Bayesian approach to the estimation for two change-point models, the constant-to-constant case and the increasing-to-constant case, also referred to as the truncated inverted bathtub shaped model. For the former model, marginal and posterior densities are obtained for both informative and noninformative priors. When noninformative priors are used, simulation results lead us to recommend some choices over others. The simulation results also lead us to make recommendations as to which estimator to use in various cases, the posterior mean or the posterior mode. Empirical Bayes and hierarchical Bayes estimation procedures are also considered. For the truncated inverted bathtub shaped model, both parametric and semiparametric approaches are considered. Simulation results again lead us to make recommendations for implementation. A brief discussion of possibile approaches to Bayesian estimation of a change-point in the mean residual life function is included in the final section.
Subject Area
Statistics
Recommended Citation
Campbell, Nancy Lee, "Bayesian models for a change-point in failure rate" (1995). ETD collection for University of Nebraska-Lincoln. AAI9604403.
https://digitalcommons.unl.edu/dissertations/AAI9604403