The fatal consequences of industrial incidents have made evident the need for suitable tools to develop inherently safer process designs. Traditionally, in a process design project, the evaluation of safety aspects is left for analysis after the detailed design has been completed. This approach leads to the use of control loops, barriers and protection layers as the only ways to prevent incidents and to reduce the possible outcomes. An alternative to this approach is the application of the concept of inherent safety, which was introduced to set up several principles that aim to enhance process safety by eliminating, avoiding or minimizing sources of risk. In this work, we present a comparison of different safety metrics in their role to evaluate the risk associated with a given process design. The indices selected for consideration are better applied at the conceptual stage of the process design, and they were the Dow's fire and explosion index (F&EI), the fire and explosion damage index (FEDI), the process route index (PRI) and the process stream index (PSI). All these indices use different input information and their outcomes have different rankings. The metrics were applied to an ethylene production process to identify risk levels, and the location of streams and pieces of equipment that pose the highest risk within the process. An evaluation of the indices in their capability to track design changes in operating conditions aiming to improve the safety level of the process was developed. To perform the assessment of the safety metrics in a more extensive manner, an uncertainty analysis based on a Monte Carlo simulation framework was implemented and compared to the traditional use of single-value design variables. Within this context, an insightful assessment of uncertainty's effect on process safety characteristics was achieved because of the identification of ranges of safetyrelevant performance outcomes (zones of risks and opportunities) that can be probabilistically characterized. The approach was applied to a case study related to the production of ethylene from shale gas. The results showed how some indexes are better suited to capture the risk characteristics associated with the process when changes in the operating conditions of the section with highest risk were implemented. The methodology can be extended to other processes of interest, and may serve as a basis for the safety and process design community to propose adjustments in the structure of the safety indices based on a better understanding of their performance and reliability as part of the efforts towards the continued improvement of those safety metrics.