Sequential Analysis, 25: 297–310, 2006
Copyright © Taylor & Francis Group, LLC
ISSN: 0747-4946 print/1532-4176 online
DOI: 10.1080/07474940600609605
A Two-Stage Procedure with Elimination for Partitioning
a Set of Normal Populations with Respect to a Control
Tumulesh K. S. Solanky
Department of Mathematics, University of New Orleans, New Orleans, Louisiana, USA
Abstract: We consider the problem of partitioning a set of given normal populations, with
respect to a control population, into two subsets according to their unknown means. In
this article, using the subset selection approach in the first stage and indifference zone
approach in the second stage, we propose a two-stage procedure. The procedure partitions
“too superior or inferior” treatments after the first stage, thereby reducing the average sample
size and making the procedure more attractive for practitioners. The proposed procedure
is studied and compared via the Monte Carlo simulation studies with other competitive
procedures known in the literature.
Keywords: Control population; Correct partition; Elimination; Simulations; Two stage
procedure.
Subject Classifications: 62J15; 62L10.
1. INTRODUCTION
Let
0
1
k
denote k + 1 independently distributed normal populations, such
that
i
∼ N
i
2
, i = 0 1 2k. We will refer to
0
as the standard or control
population. We will assume that
i
’s and are all unknown, with
i
∈ R, ∈ R
+
,
i = 0 1 2k.
The goal is to partition the set of treatments =
i
i = 1 2k, into two
disjoint and exhaustive subsets, corresponding to the “good” and “bad” populations
compared with the control population
0
, as defined later, and with a prespecified
probability of correct partition. That is, given arbitrary but fixed constants
1
and
Received May 27, 2004, Revised November 23, 2004, Accepted February 10, 2005
Recommended by P. Chen
Address correspondence to Tumulesh K. S. Solanky, Department of Mathematics,
University of New Orleans, New Orleans, LA 70148, USA; E-mail: tsolanky@uno.edu