Majority of pipeline infrastructure are old and susceptible to possible catastrophic failures due to fatigue. Timely maintenance is the key to keep pipeline in serviceable and safe condition. This paper proposed a Bayesian inference methodology based on the observed crack growth measurements and cycle data that predicts the probability density of failure after initially estimating the equivalent initial flaw size (EIFS). The model was first developed based on one-dimensional crack growth problem in plate with edge crack. Then the model was expanded to two-dimensional crack growth problem in pipe wall. Stress intensity factors (SIF) at the crack tip in pipe model were calculated using finite element (FE) analysis for different crack lengths and depths. Polynomial function and Gaussian process were used to develop surrogate models of SIF. The analysis demonstrated that the proposed Bayesian inference method with hyperparameters generated accurate inferred results for probability density function (PDF) of both EIFS and the number of cycles to failure.