This paper describes the Maximum Likelihood Estimator and the Bayesian using gamma prior Estimator of the Weibull distribution based on interval censored data. The Bayesian estimates of the survival and hazard functions we can’t solve it analytical for that Gauss Quadrature method is used to estimate the survival and hazard functions. Also Lindley’s approximation is used. The two methods are compared to maximum likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) and absolute bias to determine the best for estimating of the survival and hazard function. Keywords: Weibull distribution, survival and hazard functions, Bayesian method, interval censored data, Gauss Quadrature, Lindley’s approximation
