Suppose components have lifetimes which follow a Weibull distribution with both scale and shape parameters unknown. Given the first r (r fixed) failure times of a sample of n components (type 2 censoring), predictions are to be made on the failure times of the remaining components in the sample (one sample prediction) and the lifetimes of unused components (two sample prediction). An outline is given of the general Bayesian approach for this problem using an informative Bayesian prior for both parameters. Iterative procedures involving considerable computation are necessary for calculating prediction bounds, but some simplification is possible on restricting the shape parameter to a finite number of values. Numerical examples are used to illustrate the procedure.