TY - JOUR
T1 - A single—stage selection procedure for multi-factor multinomial experiments with multiplicativity
AU - Bechhofer, Robert E.
AU - Goldsman, David M.
AU - Jennison, Christopher
N1 - Funding Information:
This research was partially supported by the U.S. Army Research Office through the iviathematicai Sciences Institute of Cornell University and by U.S. Army Research Office Contract DAAL03-86-Ic-0046 at Cornell University. The writers are indebted to Professor Santner for his constructive comnents. We also wish to thank Ms. Katliy King for her expertise in typing this manuscript.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 1989/1/1
Y1 - 1989/1/1
N2 - . A single—stage procedure is proposed for selecting the event which has the largest probability in multi—factor multinomial experiments with multiplicativity, i.e., experiments in which the factor—level responses of any one factor are independent of those of all other factors. The procedure is a generalization of one proposed for single—factor multinomial experiments by Bechhofer, Elmaghraby and Morse (B— E—M) (1959). Tables necessary to implement the procedure are provided, and properties of the procedure are obtained. It is shown that if independence holds it is much more efficient in terms of minimizing total sample size to conduct the experiment as a factorial experiment rather than as independent single—factor experiments. Specifically, if an f—factor (f > 2) experiment is conducted, and certain symmetry conditions hold, the factorial experiment requires 1/f as many observations to guarantee the same indifference—zone probability requirement, as do f independent single-factor experiments. If multiplicability does not hold the experimenter can use the original B-E-M single-stage, single-factor procedure but for a different goal and probability requirement than the one employed for the 2-factor problem.
AB - . A single—stage procedure is proposed for selecting the event which has the largest probability in multi—factor multinomial experiments with multiplicativity, i.e., experiments in which the factor—level responses of any one factor are independent of those of all other factors. The procedure is a generalization of one proposed for single—factor multinomial experiments by Bechhofer, Elmaghraby and Morse (B— E—M) (1959). Tables necessary to implement the procedure are provided, and properties of the procedure are obtained. It is shown that if independence holds it is much more efficient in terms of minimizing total sample size to conduct the experiment as a factorial experiment rather than as independent single—factor experiments. Specifically, if an f—factor (f > 2) experiment is conducted, and certain symmetry conditions hold, the factorial experiment requires 1/f as many observations to guarantee the same indifference—zone probability requirement, as do f independent single-factor experiments. If multiplicability does not hold the experimenter can use the original B-E-M single-stage, single-factor procedure but for a different goal and probability requirement than the one employed for the 2-factor problem.
KW - market research sampling
KW - multinomial selection problem
KW - multiplicative probability matrix
KW - ranking procedures
KW - selection procedures
KW - single—stage procedures
UR - http://www.scopus.com/inward/record.url?scp=84949364764&partnerID=8YFLogxK
U2 - 10.1080/03610918908812746
DO - 10.1080/03610918908812746
M3 - Article
AN - SCOPUS:84949364764
VL - 18
SP - 31
EP - 61
JO - Communications in Statistics - Simulation and Computation
JF - Communications in Statistics - Simulation and Computation
SN - 0361-0918
IS - 1
ER -