Abstract: As the development of the technology and material science, products become highly reliable with long lifetimes. Consequently, the traditional life tests are gradually replaced by the degradation tests. In the degradation tests, the quality characteristic (QC) which degrades over time, can reflect the reliability status of the product. Some of the degradation paths of the QC are usually monotonically increasing and non-smooth function of time. In this paper, motivated by the degradation data from the tests of N-channel power metal oxide semiconductor field-effect transistor (MOSFET), we propose a two-phase gamma process under hierarchical Bayesian framework to model the monotonic and non-smooth degradation data. A simulation study is performed to verify the utility of the proposed model under three scenarios. An illustrative anti-radiation performance case study is analyzed to show the applicable power of the proposed model.