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???(2?2?????)) ???? 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)