This book provides both the assessment of repairable system reliability using the proportional intensity models and a thorough evaluation on the model performance for a set of special engineering applications, including right-censoring severity, life cycles with substantial overhaul (dormancy) intervals, and multiple failure types (major and minor). Compared to the extensive literature on application of the Cox-based PI regression models in the biostatistics field, there has been a small but growing body of literature reported for reliability engineering applications. The robustness study simulates recurrent failure data, and provides a thorough examination across a relevant range of sample size, shape parameter, and censoring severity values. Cox-based proportional intensity models include PWP-GT, PWP-TT, AG, and WLW models. The results are beneficial to practitioners in anticipating the more favorable applications domains and selecting appropriate PI models.