The aim of this study is to estimate the robust survival function for the Weibull distribution. Since the survival function of Weibull distribution is based on the parameters, we consider two robust and explicit Weibull parameter estimators proposed by Boudt et al. (2011). The quantile and the quantile least squares which are all robust to censored data is used as an alternative to the maximum likelihood estimation of the Weibull parameters. The proposed estimators are applied to Hodgin's disease data which produces smaller variances for the robust survival function. The advantage of new methods is that they are numerically explicit in applications. Monte Carlo simulation is performed to compare the behaviours of the proposed robust estimators in the presence of right, left and interval censored observations considering different censoring rates. The simulation results show that the proposed robust estimators are better than the maximum likelihood estimator.