Full Estimation Capacity Hierarchical Fractional Factorial Designs for a Class of Models

Abstract

This article presents the characterizations of full estimation capacity (FEC) of the general hierarchical fractional factorial designs under a class of possible models for describing the data to be collected from planned experiments. The experimenter may not be sure what model will describe the data to be collected a priori but will suggest a class of possible models so that one model provides a better description than the others. The hierarchical designs (HDs) permit the estimation of different model parameters using its component designs. A general HD is presented for a 2^m factorial experiment. The FEC properties are demonstrated under a variety of situations in terms of the number of runs.

Keywords:

• Fractional factorial
• Full estimation capacity
• Hierarchical designs
• Two-factor interactions
• Unbiasedly estimable

Mathematics Subject Classification:

• Primary 62K15; Secondary 62J05; 62K99; 62J99