TABLE 2.

Sets of events for K‐arm J‐stage design with $k\in \{1,\dots ,K-1\}$

Set	Definition
$C_j^{(k)}$	$\{l_{j-1}^{(k)}<Z_{j-1}^{(k)}<u_{j-1}^{(k)}\}$
$S_j^{(k)}$	$\{Z_{j-1}^{(k)}\le l_{j-1}^{(k)}\}$
$E_j^{(k)}$	$\{\left((C_j^{(1)}\cup S_j^{(1)})\cap \overline{(C_j^{(k)}\cup S_j^{(k)})}\right)\cup (E_j^{(k-1)}\cap C_j^{(k)}\left)\right\}$
$E_j^{(0)}$	$\mathrm{\Omega }$
$A_{j,1}^{(k)},k>0$	$E_j^{(k)}$
$A_{j,2}^{(k)},k>1$	$E_j^{(k-1)}\cap S_j^{(k)}$
$A_{j,k+1-s}^{(k)},k>2,s=1:k-2$	$E_j^{(s)}\cap {S_j^{(s+1)}\bigcap }_{t=s+2}^k(C_j^{(t)}\cup S_j^{(t)})$

Note: $\mathrm{\Omega }$ is the whole sample space.