Bayesian Nonparametric Estimation in A Series System or a Competing-Risks Model Ram Tiwari National Cancer Institute          Abstract: This paper presents a Bayesian nonparametric approach to the estimation of a system and its components’ survival functions arising from observing the failure of a series system or a competing-risks model. A Dirichlet multivariate process is used as a prior for the vector of the components’ random subsurvival function to derive the Bayes estimator of the survival function when the cause of failure belongs to a certain risk subset. The weak convergence and the strong consistency of the estimator are established. The special case when the system has only two components corresponds to well studied randomly censored model.