This paper addresses the issues in setting performance criteria for safety regulation of nuclear power plants. Since setting criteria at the low level is a much more difficult task than it is at the top level, the low-level performance criteria should be derived consistently from the more easily determinable top-level performance criteria. The paper also proposes several approaches to characterizing uncertainties in performance criteria, by extending the reliability allocation methodology that is based on the mean-to-mean mapping to a stochastic multi-objective optimization problem where the state variables are uncertain.