Semi-parametric Shared Frailty Model Based on MCMC Method and its Application in Reliability

• To mitigate the limitation of the traditional hypothesis that the lifetimes of the individuals obey the independent identically distribution, the semi-parametric shared frailty model based on the developmental proportional hazards model with frailty was constructed, which can reflect the influence caused by the random effect . In this model, the baseline hazard was supposed to be piecewise constant hazard. Then the MCMC method based on Gibbs sampling to simulate dynamically the Markov Chain of the parameters’ posterior distribution was brought forward. By that the parameters’ Bayesian estimations under the condition of the random truncated test and the prior distribution of the frailty belongs to the Gamma distribution were given out. Also the martingale process of the baseline hazard was introduced , as well as the precision of the numeration was improved. What’s more, an application of these techniques was illustrated by an example.

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