Cyber-Physical Systems (CPS) often involve complex networks of interconnected software and hardware components that are logically combined to achieve a common goal or mission, for example, keeping a plane in the air or providing energy to a city. Failures in these components may jeopardise the mission of the system. Therefore, identifying the minimal set of critical CPS components that is most likely to fail, and prevent the global system from accomplishing its mission, becomes essential to ensure reliability. In this paper, we present a novel approach to identifying the Most Likely Mission-critical Component Set (MLMCS) using AND/OR dependency graphs enriched with independent failure probabilities. We address the MLMCS problem as a Maximum Satisfiability (MaxSAT) problem. We translate probabilities into a negative logarithmic space in order to linearise the problem within MaxSAT. The experimental results conducted with our open source tool LDA4CPS indicate that the approach is both effective and efficient. We also present a case study on complex aircraft systems that shows the feasibility of our approach and its applicability to mission-critical cyber-physical systems. Finally, we present two MLMCS-based security applications focused on system hardening and forensic investigations.