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In many real life scenarios, stress accumulates over time and the system fails as soon as the accumulated stress or degradation equals or exceeds a critical threshold. For some devices, it is possible to obtain measurements of degradation over time, and these measurements may contain useful information about product reliability. In general, any parametric methodology is potentially sensitive to the assumed degradation model and the resulting estimator may be biased whenever the choice of the parametric form is incorrect. In this paper, we propose a semi-parametric random effect (frailty) model for degradation path, and a method of estimating this path as well as the reliability. Consistency of the estimator under general conditions is established. Simulation results show superiority of the performance of the proposed method over a parametric competitor. The method is illustrated through the analysis of a real data set.
Two-stage regression methods are quite popular for analysing the simultaneous equations models in economics and social sciences. However, the estimation of the model parameters is challenging when response and/or the endogenous covariate(s) contain excess zeros. In this paper, a Bayesian approach for the joint modeling of a zero-inflated longitudinal continuous response and a zero-inflated count endogenous covariate is proposed. We define latent continuous variables for handling the excess zeros and develop a Gibbs sampler for the simultaneous estimation of the model parameters for both the models. The method is illustrated with an analysis of real data from the health and retirement study. Simulation studies are performed for assessing the usefulness of the proposed method compared to its competitors. The proposed method will be useful in biomedical research, economic research and studies related to the social sciences. |