The study was carried out to provide a general procedure to estimate censored data. Parameters in censored data are not estimated in the same way that those in uncensored data are. Problems in estimating survival time events are compounded due to inappropriate choice of starting time in survival studies. Normalized spacingprocedure for handling censored data are investigated by using the proposed generalized model. Survival times are arranged to start from time zero and thereby eliminating truncations in the algorithm. Recursive partitioning for placing of the survival time are used to normalize spacing of intervals so that at least an event time (failure time) is located in every interval for easy possible parameter estimation. Simulations showed that the generalized algorithm developed was better and adequate.