About the reliability of circuits under failures of type $0$ at the outputs of elements in a complete finite basis containing some pairs of functions

We consider the realization of Boolean functions by the circuits from unreliable elements in a complete finite basis containing some pairs of functions. We assume that all elements of a circuit are exposed to the faults type $0$ at the outputs with probability $\varepsilon \in (0,1/2)$ independently of each other. We prove that almost any Boolean function can be implemented by an asymptotically optimal in reliability circuit functioning with the unreliability which is asymptotically equal to $\varepsilon$ with $\varepsilon \to 0$.