Longitudinal inspections of thickness at particular locations along a pipeline provide useful information to assess the lifetime of the pipeline. In applications with different mechanisms of corrosion processes, we have observed various types of general degradation paths. We present two applications of fitting a degradation model to describe the corrosion initiation and growth behavior in the pipeline. We use a Bayesian approach for parameter estimation for the degradation model. The failure-time and remaining lifetime distributions are derived from the degradation model, and we compute Bayesian estimates and credible intervals of the failure-time and remaining lifetime distributions for both individual segments and an entire pipeline circuit.