Strength reliability of ceramics depends on accuracy of parameters involved in the probability distribution function for fracture. The parameters are usually estimated by use of strength data. However, one may have additional information in the experiment, such as fracture cause data, fracture location data, flaw-size data and flaw-orientation data. In this paper, we will incorporate these additional information in the parameter estimation to improve the accuracy of the reliability. A new theory on the asymptotic variances is presented.