We use Bayesian methods to fit a lognormal mixture model with two components to right censored survival data to estimate the survivor function. This is done using a simulation-based Bayesian framework employing a prior distribution of the Dirichlet process. The study provides an MCMC computational algorithm to obtaining the posterior distribution of a Dirichlet process mixture model (DPMM). In particular, Gibbs sampling through use of the WinBUGS package is used to generate random samples from the complex posterior distribution through direct successive simulations from the component conditional distributions. With these samples, a Dirichlet process mixture model with a lognormal kernel (DPLNMM) in the presence of censoring is implemented.