Explosive desorption is a desorption mechanism in response to impulsive grain heating, which triggers exothermic chemical reactions between free radicals within an ice mantle. This mechanism has been suggested as one of viable desorption mechanisms to explain the presence of complex organic molecules (COMs) in cold environments. However, despite theoretical / laboratory dedications on this topic over the last few decades, there is no clear consensus on how critically this process contributes to the observed gas-phase abundances. To tackle this problem, here we have constructed a model that treats the physics and chemistry of the composite ice mantle as a thermodynamic system composed of H2O, CO, CO2, and embedded radicals to better represent the interstellar ice. With this new model, we explored a critical combination of parameters that determines explosive threshold. Explosive desorption takes place when 1) the impulsive grain heating efficient enough to increases initial temperature above 20K, 2) the radical concentration is as high as ~1% with respect to water ice, and 3) the representative diffusion binding energy of radicals in the ice is lower than ~1000K. Thus the efficiency of explosive desorption varies depending on the grain size and the chemical composition of ice, especially the concentration of atomic H.