An internal combustion engine arrangement includes an internal combustion engine, a catalytic converter, and a controller. The controller is configured to determine a maximum H2 production capacity of the catalytic converter. The catalytic converter is arranged downstream of the internal combustion engine. The controller is configured and adapted to determine the maximum H2 production capacity of the catalytic converter based on a first function that correlates an H2 production of the internal combustion engine with first internal combustion engine parameters.