This paper presents an application of L-moment statistics and the respective L-moment ratio diagrams (LMRD) to assess control performance, in particular, in terms of control system sustainability. L-moment diagrams are common in extreme events analysis and are considered a very powerful tool in this field at the regional level. Control system assessment is a well-established research area that investigates approaches and methodologies for measuring the quality of control systems. Statistical moments can be used to assess the effectiveness of control systems. The same principle applies to L-moments, with a possible further application to the assessment of control system robustness. The incorporation of the time impact into the analysis allows us to examine the evolution of control systems. In this context, measuring sustainability is only one step away. In this research, L-moments and L-moment ratio diagrams are used to assess the quality of PID-based control systems. In addition, the evolution of their performance over time is depicted visually. Moreover, a robust discordance measure is proposed to measure the robustness, evolution, and sustainability of control systems. The proposed approach is successfully validated using real industrial data obtained from PID basic regulatory control within the hierarchical advanced process control (APC) structure of a large ammonia production plant.