A new reliability model, consecutive 2-out-of-(r, r)-from-(n, n):F model, is proposed. The consecutive 2-out-of-(r, r)-from-(n, n):F system consists of a square grid of side n (containing n2 components) such that the system fails if and only if there is at least one square of side r which includes among them at least two failed components. For independent, identically distributed case an algorithm is given for computing the reliability of the system. The reliability function can be expressed by the number of 0–1 matrices having no two or more 0s at any square of side r.
