Component failures can result in catastrophic behaviors in safety critical embedded systems, sometimes resulting in loss of life. Component failures can be treated as off nominal behaviors (ONBs) with respect to the components and sub systems involved in an embedded system. A lot of research is being carried out to tackle the problem of ONBs. These approaches are mainly focused on the states (i.e., desired and undesired states of a system at a given point of time to detect ONBs). In this paper, an approach is discussed to detect component failures and critical components of an embedded system. The approach is based on fault tree analysis (FTA), applied to the requirements specification of embedded systems at design time to find out the relationship between individual component failures and overall system failure. FTA helps in determining both qualitative and quantitative relationship between component failures and system failure. Analyzing the system at design time helps in detecting component failures and critical components and helps in devising strategies to mitigate component failures at design time and improve overall safety and reliability of a system.