Suppose we have a set $S$ consisting of $p$ features, and a subset $S_+$ of the features are positive. If $Q$ is any subset of $S$, define the false positive rate as the proportion of features in $Q$ which are not positive:
$$FPR[Q] = 1 - \frac{|Q \cap S_+|}{|Q|}$$
where $|\cdot|$ denotes cardinality. If $Q$ is a function of the data, $d$, then we can define the false discovery rate as the expected false positive rate:
$$FDR[Q(d)] = \mathbb{E}_d[FPR[Q(d)]].$$
Now suppose that I have a method for ranking the features in $S$ by likelihood of significance. I will report the top $r$ features most likely to be significant, based on my data, $Q_r(d)$. Formally, I have a family of set-valued functions
$$Q_1(d) \subset Q_2(d) \subset Q_3(d) \subset \cdots \subset Q_p(d)$$
where $|Q_r(d)| = r.$
What I want to know is the maximum $r$ such that the set $Q_r$ has a false discovery rate less than a certain critical value, $q_{crit}$. That is, I want to know what is the value
$$IFDR_{q_{crit}} = \max_r \{r \in \{1,...,d\}: FDR[Q_r] \leq q_{crit}\}$$
Is there a name for this 'inverse false discovery rate' function? If not, can you suggest a name better than 'inverse false discovery rate'?