In the survival analysis, when there is a cure fraction and the occurrence times of events are correlated, the cure frailty model is utilized. The main objective is to propose a method of analysis for two types of correlated frailty in the non-mixture cured model in order to separate the individual and shared heterogeneity between subjects. The cure models with correlated frailty and promotion time are considered. In both models, the likelihood function are based on piecewise exponential distribution for hazard function. To estimate the parameters, hierarchical Bayesian modeling is employed. Due to non-closed forms of the posteriors, they are estimated by MCMC algorithms. The Cox correlated frailty model is used as a benchmark and models are compared by DIC Criterion . The results show the superiority of cure models with correlated frailty.