On checking tests for a parity counter

We consider the circuits of functional elements realizing the Boolean function
$$ f^{\oplus }_{n}(\tilde{x})=x_{1}\oplus x_{2}\oplus \ldots \oplus x_{n} $$
under arbitrary constant failures on the inputs of elements. It is proved that for such circuits the length of the complete checking test is no less than $n+1$. It is shown that there exists a circuit realizing $f^{\oplus }_{n}(\tilde{x})$ with the complete checking test of length $n+2$.