Objective: The purpose of this study is to determine the models expressing ideally the recurrent events data encountered in the survival analyses. In this study, the frailty model, which is used in the survival analysis to explain the heterogeneity that both modeling of recurrent events and latent risk factors cause, has been explained in detail. The heterogeneity stemming from genetics or unmeasured covariates has been modeled with adduct of unmeasured random effect to the hazard model. Material and Methods: In this study, exacerbation-free survival of chronic obstructive pulmonary disease (COPD) patients were estimated by Kaplan -Meier method. Data of recurrent exacerbations were analysed using frailty models, which are employed for repeated failures. Among frailty distributions, gamma, inverse gaussian, lognormal and positive stable distributions are considered. Fit criteria, namely Akaike information criterion (AIC) and Bayesian information criterion (BIC), as well as graphical assessment are collectively utilized in order to determine the optimal distribution model. Ultimately, the Weibull regression model was chosen to analyse the data regarding COPD patients who experienced repeated failures. Gamma distribution was selected for frailty term and the frailty model is built. Results: The frailty model for the COPD exacerbations showed that p values for mMRC variable (p<0.0001) and FEV1 variable (p<0.0001) were both significant. Latent risk factors environmental and genetic factors other than mMRC and FEV1 may effect the time to failure of COPD patients. It may be suggested that such concealed factor or factors impose 3.5 times increased risk for exacerbation in a given COPD patient. Conclusion: In conclusion, the frailty models can be used in the modeling of recurrent events in the survival analysis, and in the explanation of heterogeneity among subjects. The explanation of this heterogeneity has dynamized the interpretation made in consequence of modeling of the survival analysis.