Bounds on Shannon functions of lengths of contact closure tests for contact circuits

We consider the problem of synthesis of irredundant two-pole contact circuits which implement $n$-place Boolean functions and allow short single fault detection or diagnostic tests of closures of at most $k$ contacts. We prove that the Shannon function of the length of a fault detection test is equal to $n$ for any $n$ and $k$, and that the Shannon function of the length of a diagnostic test is majorized by $n+k(n-2)$ for $n\geqslant 2$.