Fragility functions are cumulative distribution functions (cdfs) of strengths at failure. They are needed for reliability analyses of systems such as power generation and transmission systems. Subjective opinions supplement sparse test data for estimating fragility functions. Often the opinions are opinions on the percentiles of the fragility function. Subjective percentiles are likely to be less biased than opinions on parameters of cdfs. Solutions to several problems in the estimation of fragility functions are found for subjective percentiles and test data. How subjective percentiles should be used to estimate subjective fragility functions, how subjective percentiles should be combined with test data, how fragility functions for several failure modes should be combined into a composite fragility function, and how inherent randomness and uncertainty due to lack of knowledge should be represented are considered. Subjective percentiles are treated as independent estimates of percentiles. The following are derived: least-squares parameter estimators for normal and lognormal cdfs, based on subjective percentiles (the method is applicable to any invertible cdf); a composite fragility function for combining several failure modes; estimators of variation within and between groups of experts for nonidentically distributed subjective percentiles; weighted least-squares estimators when subjective percentiles have higher variation at higher percents; and …