Probabilistic seismic hazard analyses are usually performed with semi-empirical ground motion models (GMMs) following the ergodic assumption whereby average source, path, and site effects from global databases apply for a specific site of interest. Site-specific site response is likely to differ from the global average conditional on site parameters used in GMMs (typically VS30 and basin depth). Non-ergodic site response can be evaluated using on-site ground motion recordings and/or one-dimensional wave propagation analyses, and allows site-to-site variability to be removed from the within-event standard deviation. Relative to ergodic, non-ergodic hazard analyses often reduce ground motions at long return periods. We describe procedures for replacing the site term in GMMs with a non-ergodic nonlinear mean over its appropriate range of periods (returning to the ergodic mean outside that range). We also present procedures for computing non-ergodic standard deviation by removing site-to-site variability while considering effects of soil nonlinearity. We illustrate application of these procedures, and their effect on hazard curves and uniform hazard spectra, as implemented in OpenSHA.