This paper presents a procedure for the reliability analysis of a multistage axial compressor regarding blade-specific roughness effects, based on the survival signature approach. As a result, a time-dependent evolution of the system reliability is obtained along with a prioritization technique for monitoring and regeneration of the rough blade rows by capturing the most critical system components. For this purpose, a one-dimensional flow model is developed and utilized to evaluate the aerodynamic influences of the blade-specific roughness on the system performance parameters, namely the overall pressure ratio and the isentropic efficiency. In order to achieve transparency and high numerical efficiency for time-dependent analyses in practice, the physics-based compressor model is translated into an illustrative, function-based system model. This system model is established by conducting a Monte Carlo simulation along with a variance-based global sensitivity analysis, with the input variables being the row-specific blade roughness. Based on the system model, the roughness impact in different blade-rows is ranked by the relative importance (RI) index, and the corresponding time-dependent reliability of the compressor system in terms of pressure ratio and efficiency is estimated through its survival function. Furthermore, uncertainties in the roughness-induced failure rates of the components are modeled using imprecise probabilities. Consequently, bounds on the reliability function and the importance indices for the blade-surface roughness in each blade row are captured, which enhances the decision-making process for maintenance activities under uncertainty.