We study the phase I analysis of data when the quality of a process or product is characterized by a linear function. We assume that simple linear regression data are available for a fixed number of samples collected over time, a situation common in calibration applications. Using a simulation study, we compare the performance of some of the recommended approaches used to assess the stability of the process. We also propose a method based on using indicator variables in a multiple regression model. We show that this method has competitive performance relative to other methods in terms of the probability of a signal for certain types of parameter shifts within the set of historical process data. We also show that two methods proposed in the literature are ineffective in detecting shifts in the process parameters. Finally, we apply some of the proposed methods to a calibration example.