 $C(P)$ which, when fault-free, implements a projective measurement of a weight-$w$ Pauli $P$ without flagging is a $t$-flag circuit if the following holds: For any set of $v$ faults at up to $t$ locations in $C(P)$ resulting in an error $E$ with $\text{min}(\text{wt}(E),\text{wt}(E P)) > v$, the circuit flags. 