This talk will cover my research in developing an efficient and robust algorithm for solving a particular problem in survival analysis. The problem is to find the nonparametric maximum likelihood (NPMLE) survival function from time-to-event data where some or all of the observation times are censored by arbitrary intervals in the positive real line. The presence of this censoring makes the problem difficult; since no closed form solution is possible, iterative optimisation techniques must be used. We have called our new algorithm the “Hierarchical Constrained Newton Method” (HCNM) because it is based on the existing CNM algorithm, enhancing it with a divide and conquer approach.