Leakage of the transmission fluid or oil in power train systems can cause engine overheating and permanent damage. Therefore, it is crucial to run a leak test to inspect for any possible porosity in the casting parts. For this purpose, a non-linear regression model is developed. The goal is to model the leak flow profiles as a function of both the leak testing time and the part temperature. The model is the following: =(0 1)(1(22)) where is the leak flow measured for part at time with temperatures (=1,,;=1,,;=1,,). is the th temperature at which part is tested, represents the testing time for recording the th measurement of the leak flow profile for part tested at its th temperature, and are independent and identically distributed random noise variables with ~(0,2)