The problem of comparing k( 2 2) bernoulli rates of success with a control is considered. An onestage decision procedure is proposed for either (1) choosing the best among several experimental treatments and the control treatment when the best is significantly superior or (2) selecting a random size subset that contains the best experimental treatment if it is better than the control when the difference between the best and the remaining treatments is not significant. We integrate two traditional formulations, namely, the indimerence (IZ) approach and the subset selection (SS) approach, by seperating the parameter space into two disjoint sets, the preference zone (PZ) and the indaerence zone (12). In the PZ we insist on selecting the best experimental treatment for a correct selection (CS,) but in the IZ we define any selected subset to be correct (CS,) if it contains the best experimental treatment which is also better than the control. We propose a procedure R to guarantee lower bounds P: for P(CS,IPZ) and Pz for P(CS211Z) simultaneously. A brief table on the common sample size and the procedure parameters is presented to illustrate the procedure R.

Two procedures for the group-testing problem based on the Shannon-entropy criteria are proposed. The model considered is that the N units are realizations of N Bernoulli independent and identically distributed (i.i.d.) chance variables with common, known probability q of an arbitrary unit being good and p =1 – q of it being defective. Both the algorithms introduced have low design complexity and yet provide near-optimal result. For N ≤ 5, one of the procedures introduced is optimal for selected values of q.

The paper studies a sequential procedure R for selecting a random size subset that contains the multinomial cell which has the largest cell probability. The stopping rule of the proposed procedure R is the composite of the stopping rules of curtailed sampling, inverse sampling, Ramsey–Alam sampling, and the truncation of fixed‐sample‐size procedure. A property on the worst configuration is shown, and it is employed in computing the procedure parameters that guarantee certain probability requirements. Tables of these procedure parameters, the corresponding probability of correct selection, the expected sample size, and the expected subset size are given for comparison.

No abstract

This paper is concerned with a closed adaptive sequential procedure for selecting a random-size subset containing experimental treatments that are better than a standard. All the k treatments under considerations are measured by two endpoints accounting for treatment efficacy and treatment safety respectively. The selection is made with regard to the two binary endpoints. An experimental treatment is considered to be better than the standard if its both endpoints have successful rates higher than the standard ones. We provide a step-by-step sampling rule, stopping rule, and decision rule for the proposed procedure. We show that the proposed sequential procedure achieves the same requirements for the probability of a correct selection as does the fixed-sample-size procedure, but requires fewer observations. We use simulations to evaluate the sample size savings of the proposed procedure over the corresponding fixed-sample-size procedure.