Corrosion is a major cause of failure in some metals with adverse effects on reliability of components and structures made from such metals. For example in carbon steel pipes various forms of localized corrosion, pitting corrosion, and stress corrosion cracking (SCC) cause sudden and catastrophic failures due to the absence of any external sign of damage in the system. Studying the growth of pit depth and pit densities at different temperatures and stress conditions with respect to time is critical in monitoring the localized corrosion damage and preventing the system downtime. A new probabilistic physics-of-failure (PPOF) model is developed to determine the temperature and stress dependencies of pit depth growth with respect to time. In doing so, microscopic methods are used to determine the pit depths produced on X-70 carbon steel samples subjected to accelerated corrosion tests. The pit depths and densities are measured in unstressed and stressed samples exposed to a solution of Sodium thiosulfate and water at different times and temperatures to ascertain the temperature and stress dependencies of pit depths that propagate during the pitting corrosion process. The stress and temperature dependency of the new model follows the exponential law (Arrhenius law), which allows estimating the activation energy of pitting corrosion process. Moreover, the pit size and intensity under different temperatures and stress conditions, estimated at different times, appear to follow the lognormal distribution. The uncertainty associated with the proposed models due to scattering of pit data and also the autocorrelation among such data are accounted for.