Consider
k( ? 2) normal populations with unknown means μ
1, …, μ
k, and a common known variance σ
2. Let μ
[1] ? ??? ? μ
[k] denote the ordered μ
i.The populations associated with the
t(1 ?
t ?
k ? 1) largest means are called the t best populations. Hsu and Panchapakesan (2004) proposed and investigated a procedure
RHPfor selecting a non empty subset of the k populations whose size is at most
m(1 ?
m ?
k ?
t) so that at least one of the t best populations is included in the selected subset with a minimum guaranteed probability P* whenever μ
[k ? t + 1] ? μ
[k ? t] ? δ*, where
P*?and?δ* are specified in advance of the experiment. This probability requirement is known as the indifference-zone probability requirement. In the present article, we investigate the same procedure
RHP for the same goal as before but when
k ?
t <
m ?
k ? 1 so that at least one of the
t best populations is included in the selected subset with a minimum guaranteed probability
P* whatever be the configuration of the unknown μ
i. The probability requirement in this latter case is termed the subset selection probability requirement. Santner (1976) proposed and investigated a different procedure (
RS) based on samples of size
n from each of the populations, considering both cases, 1 ?
m ?
k ?
t and
k ?
t <
m ?
k. The special case of
t = 1 was earlier studied by Gupta and Santner (1973) and Hsu and Panchapakesan (2002) for their respective procedures.
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