A restricted subset selection rule for selecting at least one of the t best normal populations in terms of their means when their common variance is known, case II

Consider k(2) normal populations with unknown means ₁,., _k, and a common known variance σ². Let _[1] ṡṡṡ _[k] denote the ordered _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 RH_pfor 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 [k-t + _1]-[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 RH_p 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 _i. The probability requirement in this latter case is termed the subset selection probability requirement. Santner (1976) proposed and investigated a different procedure (R_S) 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.