In this paper, we discuss the tolerance analysis methods for the component with a mean shift or drift. A new tolerance analysis model that assumes the mean shift in normal distribution rather than in uniform distribution is proposed. Simulation shows that the difference between the uniform distribution and normal distribution is 1.7%, which can be ignored, for mean shift to one standard deviation (σ). However, the difference becomes significant when the mean shift increases. The difference increases to 5.2% with 1.5σ shift, to 10.9% for 2σ shift, and up to 30.4% for 3σ shift. As normal distribution is a better model for statistical mean shift in manufacturing process, this investigation shows that the proposed tolerance analysis model can give a better model compared to conventional models.