Probabilistic seismic hazard analysis （PSHA）, the most widely used method for assessing seismic hazard and risk, contains an error in its hazard calculation; incorrectly equating the conditional exceedance probability of the ground-motion attenuation relationship （a function） to the exceedance probability of the ground-motion uncertainty （a variable）. This error results in using the ground-motlon uncertainty （spatial characteristic） to extrapolate occurrence of ground motion （temporal characteristic） or the ergodic assumption. This error also results in difficulty in understanding and applying PSHA. An alternative approach, called KY-PSHA, is developed to correct the error in this paper.