This paper describes statistical procedures for characterizing and accounting for uncertainty in earthquake fragility models. Both fully analytical and non-parametric bootstrap methods are used to describe the conditional probability distribution of damage exceedance given an intensity measure. This enables the development of confidence intervals for fragility curves for any confidence level of interest. When analyzing annual collapse rate, the uncertainty in fragility curves gets propagated when integrated with the seismic hazard curve. This study therefore proposes methods to estimate the moments as well as the full distribution of the resulting annual damage exceedance rate. This is a significant improvement from current practice, which only use the “expected fragility” to integrate with the hazard curve, thus producing a single value for annual collapse rate. Using an example for a building analyzed through incremental dynamic analysis for a site in Oakland CA, this study demonstrates the significant uncertainty surrounding the annual collapse rate and demonstrates simplified methods to characterize this uncertainty through a closed-form beta-distribution model.

Keywords: Fragility curves, uncertainty modeling, beta distribution, bootstrap method