Restricted subset selection and its application

This paper develops procedures for selecting a set of normal populations with unknown means and unknown variances such that the final subset of selected populations satisfies the following requirement: with probability at least P^*, the selected subset will contain a population or ‘only and all’ of those populations whose mean or means are within a value of d^* from the smallest mean. The size of the selected subset is random; however, at most, m populations will be chosen. A restricted subset attempts to exclude populations that deviate more than d^* from the smallest mean. Here P^*, d^*, and m are user-specified parameters. These procedures can be used when the unknown variances across populations are unequal. We then extend the sequentialized procedure to perform a selection with constraints. An experimental performance evaluation demonstrates the validity and efficiency of these restricted-subset-selection procedures.