The proportional hazard model is the most general of the regression models since it is not based on any assumptions concerning the nature or shape of the underlying survival distribution. The model assumes that the underlying hazard rate is a function of the covariates (independent variables) and there are no assumptions about the nature or shape of the hazard function. Proportional hazards model in survival analysis is used to estimate the effects of different covariates which was influenced by the survival data. This paper proposes the new multiplicative piecewise gamma in the hazard function using OpenBugs Statistical Packages. The proposed model is a flexible survival model for any types of non-informative censored data in estimating the parameters using Bayesian approach and also an alternative model to the existing model. We used the Markov Chain Monte Carlo method in computing the Bayesian estimator on leukemia data. The results obtained show that the proposed model can be an alternative to the existing multiplicative model since it can estimate the parameters using any types of survival data compared to the existing model that can only be used for leukemia data.