【Abstract】  We consider the simulation optimization problem of selecting the best system design from a finite set of alternatives, which is known as ranking and selection (R&S). Many fully sequential procedures have been proposed to solve the R&S problem using a static sampling rule in order to ensure a finite-sample statistical guarantee. In this paper, we develop fully sequential procedures that can incorporate various adaptive sampling rules, based on a modification of Paulson’s bound Paulson (1964), while still preserving the finite-sample guarantee. In particular, we propose an adaptive sampling rule that utilizes the consecutively updated sample mean and sample variance information by solving a minimization problem of the approximated total sample size. Finally, we demonstrate the efficiency of the proposed procedures with several existing procedures through extensive simulation experiments, and apply them to solve an ambulance dispatching problem.