On two-stage selection procedures and related probability-inequalities

‘Some tactical problems in digital simulation’ for the next 10 years

“…But comparisons of all pairs of differences after each incremental replication can create a significant coordination bottleneck: When P > k not all available processors will even be used; and when k P all processors will be repeatedly idle during the nontrivial work of doing k(k − 1)/2 comparisons. Contrast this with a simple two-stage procedure, such as Rinott (1978), that can be implemented to avoid any coordination at all because the number of replications generated from scenario x i depends only on scenario x i . The penalty is that substantially more replications are needed to select the best for typical problems, which may limit the size of problem that can be solved in a timely manner, or greatly increase the cost for processors when the number of scenarios k is huge and much larger than P.…”

Sequential selection procedures: Using sample means to improve efficiency

“…The two-stage procedure of Rinott (1978) has been widely studied and applied. Let n 0 be the number of initial replications or batches.…”

“…where z is the smallest integer that is greater than or equal to the real number z, and h (which depends on k, P * , and n 0 ) is a constant that solves Rinott's (1978) integral (h can be calculated by the FORTRAN program rinott in Bechhofer et al (1995), or can be found from the tables in Wilcox (1984)). We then compute the overall sample meansX i (N i ) = N i j=1 X ij /N i , and select the design with the smallestX i (N i ) as the best one.…”

Multiobjective simulation-based methodologies for medical decision making.

“…R&S can handle comparison with not common variance. We will use Rinott's (1978), it used when variances are unknown; it is two-stage R&S procedure; the two stages of sampling guaranteed PCS. Rinott's (1978) procedure:…”

“…Thus we utilized a RankingSelection procedure of Rinott, (1978), to select the system with the largest expected performance measures (Bechhofer 1995, Kim-Nelson 2001, Nelson-Miler 1995.…”