Sensitivity and uncertainty analyses of molten core cooling under the ex-vessel phase of a severe accident of a light water reactor was performed with the COOLAP-I (COOLability Analysis Program-I) model, a parametric model considering one-dimensional heat transfer of a porous debris particle bed, covering a broad range of phenomena from the melt jet release to the long-term cooling process. COOLAP-I improved the previous version by including particle generation by the fuel-coolant interaction (FCI), and internal heat generation by the decay heat. With nine representative input parameters, an uncertainty analysis using Latin hypercube sampling (LHS) method with 300 samples were conducted, and the cooling characteristics such as total enthalpy, maximum temperature, decay heat ratio, and cake (a lump of connected particles) fraction, were examined for the elapsed time of up to 50 h. This analysis demonstrates the impacts of the water pool depth, the jet breakup-related parameters, and the accumulation area of the debris particles on the cake formation by particle agglomeration and analyzes the long-term coolability of debris particle bed in plant scale conditions.