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This study is concerned with the impact of components' failure on the controllability of an automated system when operating. The work proposes a method based on a graph-theoretic approach to study the controllability of systems whose only the structure is known. The study focuses on the actuators' failures and assumes that their probabilities are known. The controllability conditions are first recalled for a linear system. One study's originality is to express the property as a Boolean equation of the actuators' set involved in the condition. A second originality of the study is to extend the definition of the reliability to cover structural properties like the controllability and to assess the probability to conserve or to lose it from the components' reliability.