A quantitative evaluation is presented of the improvement in reliability which can be achieved in a digital system by the use of redundancy and restoring organs. Three measures of reliability are considered. Two types of restoring organs, majority vote takers and adaptive vote takers are considered. For the case of majority vote takers simple expressions have been developed for the approximate relationships between the amount of redundancy, the number of vote takers, and the corresponding improvement in system reliability. The analysis includes the case of redundant nonperfect vote takers, and the optimum number of imperfect vote takers (of known reliability) to be used in any system has been established.