In the pharmaceutical industry, the shelf life of a drug product is determined by data gathered from stability studies and is intended to provide consumers with a high degree of confidence that the drug retains its strength, quality, and purity under appropriate storage conditions. In this paper, we focus on liquid drug formulations and propose a Bayesian approach to estimate a drug product's shelf life, where prior knowledge gained from the accelerated study conducted during the drug development stage is used to inform the long-term study. Classical and nonlinear Arrhenius regression models are considered for the accelerated conditions, and two examples are given where posterior results from the accelerated study are used to construct priors for a long-term stability study.