Prediction of remaining useful life using the field monitored performance data provides a more realistic estimate of life and helps develop a better asset management plan. The field performance can be monitored (indirectly) by observing the degradation of the quality characteristics of a product. This paper considers the gamma process to model the degradation behavior of the product characteristics. An integrated Bayesian approach is proposed to estimate the remaining useful life that considers accelerated degradation data to model degradation behavior first. The proposed approach also considers interaction effects in a multi-stress scenario impacting the degradation process. To reduces the computational complexity, posterior distributions are estimated using the MCMC simulation technique. The proposed method has been demonstrated with an LED case example and results show the superiority of Bayesian-based RUL estimation.