This paper presents a novel approach to the reliability modeling and analysis of a component-based system that allows dealing with multiple failure modes and studying the error propagation among components. The proposed model permits to specify the components attitude to produce, propagate, transform or mask different failure modes. These component-level reliability specifications together with information about systems global structure allow precise estimation of reliability properties by means of analytical closed formulas, probabilistic model-checking or simulation methods. To support the rapid identification of components that could heavily affect systems reliability, we also show how our modeling approach easily support the automated estimation of the system sensitivity to variations in the reliability properties of its components. The results of this analysis allow system designers and developers to identify critical components where it is worth spending additional improvement efforts.