The existing fleet of nuclear power plants is in the process of having its lifetime extended and having the power generated from these plants increased via power uprates and improved operations. In order to evaluate the impact of these factors on the safety of the plant, the Risk-Informed Safety Margin Characterization (RISMC) pathway aims to provide insights to decision makers through a series of simulations of the plant dynamics for different initial conditions and accident scenarios. This paper presents a case study in order to show the capabilities of the RISMC methodology to assess the impact of power uprate of a boiling water reactor system during a station blackout accident scenario. We employ a system simulator code, RELAP5-3D, coupled with RAVEN, which performs the stochastic analysis. Our analysis is performed by (a) sampling values from a set of parameters from the uncertainty space of interest, (b) simulating the system behavior for that specific set of parameter values, and (c) analyzing the outcomes from the set of simulation runs.