Pitting corrosion is a localized corrosion that often causes leak and failure of process components. The aim of this work is to present a new fitness-for-service (FFS) assessment methodology for process equipment to track and predict pitting corrosion. In this methodology, pit density is modeled using a non-homogenous Poisson process and induction time for pit initiation is simulated as the realization of a Weibull process. The non-homogenous Markov process is used to estimate maximum pit depth, considering that only the current state of the damage influences its future development. Subsequently, the distributions of the operating pressure and the estimated burst pressure of the defected component are integrated with Monte Carlo simulations and First Order Second Moment (FOSM) method to calculate the reliability index and probability of failure. This methodology provides a more realistic failure assessment and enables consideration of uncertainty associated with estimating pit characteristics. The practical application of the proposed model is demonstrated using a piping case study.