Sequential selection procedures for choosing the better of two binomial populations
Let π1 and π2 be binomial populations with success probabilities p1 and p2, respectively. Assume without loss of generality that p1 ≥ p2. Several papers have appeared which have compared sequential vector-at-a-time (VT) and play-the-winner (PW) sampling schemes for choosing the better of the two populations under an indifference zone approach. These schemes choose π1 with probability at least P∗, a preassigned value, as long as p1−p2 > Δ∗ ≥ 0 (Δ∗-condition) where Δ∗ is also a preassigned value. This paper presents VT and PW sampling schemes which relax the Δ∗-condition on the parameter space by employing a subset selection approach. Here, a subset of populations is chosen such that with probability P∗, a preassigned value, π1 is included in the subset. Exact and approximate formulas are derived for the probability of including π1 in the subset, the expected sample size and the expected number of populations selected [E(S∣R)]. In addition, it is shown that for all procedures, E(S∣R) can be bounded above by...