As a rule of thumb, power law process is always used to model the reliability growth process. With the test, find and fix process proceeding, the potential failure modes are surfaced, the failure mechanics are analysed and the fixes are incorporated. Thus, the system reliability is improving. Given the failure data acquired from this process, power law process is widely used to depict this reliability growth. Statistical inference for the parameters of the power law process has been proposed, e.g. maximum likelihood estimate. With computation of computers growing and packages available, Bayesian inference attracts more attention. Among these multiple packages, the BUGS (Bayesian inference using Gibbs Sampling) package is a free and a relatively easy tool that estimates the posterior distribution of the parameters of interest. In this paper, we focus on the Bayesian method to tackle the power law process inference. The power law process and the Gibbs sampling were introduced. Through the simulation data, different prior information was utilized and the inference results were compared. A field automotive data was also used to demonstrate this method. Case study has shown that the Bayesian inference is an alternative method and the computation is relatively easy with the help of the BUGS package.