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Fragility functions are an important tool in earthquake engineering, used to compute the probabilities of different damage states as a function of seismic response. They can be developed for large systems like buildings and bridges, as well as for individual structural and non-structural components, such as those used in the FEMA P-58 Seismic Performance Assessment Procedure. There are currently a number of problems associated with some P-58 non-structural mechanical component fragility functions and related loss predictions, including non-convergence when fitting the fragility functions in some cases and non-monotonic loss predictions. In this study, we recommend improvements to these fragility functions and loss predictions. Firstly, we recommend using the maximum likelihood method to fit the fragility functions to the underlying empirical data. This mitigates the non-convergence problems when …