Probabilistic methods developed at Garrett Auxiliary Power Division of Allied-Signal Aerospace Company under the “Life Prediction Methodology for Ceramic Components of Advanced Heat Engines” program sponsored by The Department of Energy/Oak Ridge National Laboratory (DOE/ORNL) under contract No. 86X-SC674C (WBS Element 22.214.171.124) are presented. Statistical methods have been developed to estimate Weibull strength parameters and component reliability with confidence limits for structural ceramics. Estimates can be made using pooled strength data from specimens of multiple sizes and loading conditions, from multiple test temperatures, and from material with multiple strength distributions. Bootstrap and likelihood ratio techniques are used to calculate confidence intervals on parameters and reliability estimates from these complex pooled data sets. A large database was generated on one ceramic (NT154 silicon nitride) to verify the methods. These statistical methods guide the development of standards for more accurate parameter estimation, to define component reliability requirements with confidence limits, and to plan specimen tests for more efficient estimation of Weibull parameters and component reliability.