Manufacturing systems with perishable products are widely observed in practice (e.g., food industry, biochemical productions, battery and semiconductor manufacturing). In such systems, the quality of the product is highly affected by its exposure time while waiting for the next operation, i.e., the residence time of intermediate parts within the system. Such a time should be strictly limited in order to ensure the product usability. The parts that reach the maximum allowable residence time need to be scrapped, thus impeding the production. To achieve an efficient production, the time-dependent or transient analysis is important to uncover the underlying principles governing production operations. In this paper, a serial production line model with two Bernoulli reliability machines, a finite buffer and perishable products is presented to analyze the transient behavior of such systems. The analytical formulas are derived to evaluate transient performance, and structural properties are investigated to study the effect of system parameters. In addition, using the model, we address problems of settling time estimation and production control to demonstrate the importance of the proposed method for transient analysis.