= Serial self-terminating search benchmark
{title2=$E[T_{\rm present}]=b+\tau(N+1)/2,\quad E[T_{\rm absent}]=b+N\tau$}
Assume $N$ candidate items are examined once each, each costs time $\tau$, nonsearch processing costs $b$, and a uniformly positioned target ends search when encountered. The target rank has mean $N^{-1}\sum_{k=1}^Nk=(N+1)/2$, proving the present-trial expression. Absent trials inspect all $N$ items. The resulting 2:1 slope ratio is a benchmark under these assumptions, not a unique diagnostic of a serial mechanism.
Back to article page
