Some applications of weighing designs

Abstract

The purpose of this paper is to apply results on weighing designs to the setting of 2 m factorial designs. Using weighing designs, we give some proposals for experimental plans. Relevant counterexamples are indicated. Also the results of a simulation study on the existence of weighing designs are presented.Key words: chemical balance weighing design, factorial design, spring balance weighing design. We now apply Theorem 3.4 (ii) for 3 0 x  . We obtain

Direct construction of globally D‐optimal designs for factors at two levels and main effects models

“…As it so happens, direct construction methods for D‐optimal designs have been available in the literature since the 1950s, usually in the context of what are called “weighing designs". These designs were generated for the initial purpose of determining the weights of objects in weighings using either a single spring balance or a chemical balance with two pans . In the “spring balance" designs, a selection of the objects would be placed on the single pan together, and the total weight recorded.…”

Some D-optimal chemical balance weighing designs: theory and examples

“…In a paper by Cheng and Kao (2015), these designs are employed in neuroimaging experiments where functional magnetic resonance imaging (fMRI) technology is used to obtain knowledge on how the brain reacts to certain mental stimuli. Another survey of common applications of weighing designs is given by Graczyk (2013).…”

On D-Optimal Chemical Balance Weighing Designs

“…Nowadays, such designs are applied in many branches of knowledge including economic survey, see Banerjee (1975), Ceranka and Graczyk (2014). Some aspects of the other applications of the chemical balance weighing designs are presented in Koukouvinos and Seberry (1997), Graczyk (2013), Katulska and Smaga (2013). Various problems related to the chemical balance weighing designs are presented in the literature.…”