More and more within the last couple of years, there is a recognition that the Web services composition concept constitute a major breakthrough and revolutionize the way we deal with integrating disparate and distributed computing environments. Yet, to rise to such a position, a chief concern is to guarantee a high-dependability level of the Web services compositions, which is significantly critical, specially in view of the particularities of the Web services environment unpredictability, heterogeneity, autonomy), if confronted with other computing environments. Our present work falls within this context since we tackle the problem of QoS (quality of service) in the Web services context by verifying to what extent fault-tolerant and dynamically-executed Web services compositions are efficiently serving their purposes. And in pursuing this goal, we introduce a novel model that characterizes, estimates and analyzes several QoS properties of dynamically-executed fault-tolerant Web services compositions - namely the reliability and the execution time. Our model allows acquiring more accurate estimations since it confers a paramount importance to the repercussions of failures. In addition, contrary to other QoS estimations models in the Web services context, which use QoS estimations published in UDDIs by the Web services owners/providers, our model computes QoS estimations on the base of the compositions execution observations, where the observation results are collected in a history. Finally, since Web services are stateless, tracking the failures and determining their locations is almost impossible. To overcome this limitation, we propose to attach to each of the composition's component a state. In doing so, obtained estimations can contribute in acquiring more accurate information about the failures locations and can be used later to improve the composition QoS in the future.