The previous literature on consecutive k-out-of-r-from-n: F systems give recursive equations for the system reliability only for the special case when all component probabilities are equal. This paper deals with the problem of calculating the reliability for a (linear or circular) consecutive 2-out-of-r-from-n: F system with unequal component probabilities. We provide two new algorithms for the linear and circular systems which have time complexity of O(n) and O(nr), respectively. The results of some computational experiments are also described.