Theoretical estimates are made of life time of Ceramic Turbocharger Rotor (CTR) for suitable mechanical design and suitable material selection. Life time of CTR is predicted taking into account the stress-temperature distribution in CTR, required failure probability, volume effect of strength and material properties. Three fatigue failure modes which are slow crack growth, oxidation, and creep failure are considered. The stress-temperature distribution in CTR in operation is estimated by means of Finite Element Method numerical analysis. The probabilistic design map is proposed as a function of turbine inlet temperature and tip speed.