In many instances protective systems used in nuclear reactors are quasi-redundant systems; each of a number of safety channels feeds a number of independent protective units. A reactor shutdown is initiated if more than a specified number of units are in favour of shut down. The objective is to achieve a very high reliability at a reasonable cost. An analysis is presented to obtain the reliability, failsafe and fail-danger probabilities of a quasi-redundant system. Three algorithms are given for: (a) the design of a quasi-redundant system having the maximum reliability subject to a cost constraint, (b) the optimal design satisfying a given reliability level at the minimum cost and (c) the optimal design satisfying a combined safety requirement at the minimum cost. The algorithms are illustrated by way of examples.