Abstract
In this paper, Resolution III saturated , factorial designs and specially the cases , , are studied, in order to obtain D-optimal plans.
Highlights
Saturated factorial plans is a very interesting issue in theory of exeprimental designs, since the reduced number of observations is very usefull in practise especially in screening experiments, where are used to determine which of many factors affects the measure of pertinent quality characteristics
In saturated designs the number of observation is equal to the number of parameters, so all degrees of freedom are consumed by the estimation of parameters, leaving no degrees of freedom for error variance estimation
There has been a considerable interest in optimal saturated main effect designs with two or three factors
Summary
Saturated factorial plans is a very interesting issue in theory of exeprimental designs, since the reduced number of observations is very usefull in practise especially in screening experiments, where are used to determine which of many factors affects the measure of pertinent quality characteristics. Chatzopoulos, Kolyva-Machera, and Chatterjee (2009), studied the optimality of designs which are obtained by adding p runs to an orthogonal array for experiments involving m factors each at s levels. Chatterjee, Kolyva-Machera, and Chatzopoulos (2011), considered the issue of optimality of fractional factorial experiments involving m factors each at two levels. Pericleous, Chatzopoulos, Kolyva-Machera and Kounias, study the problem of estimating the standardized linear and quadratic contrasts in fractional factorials with k factors, each at 3 levels, when the number of runs or assemblies is N = 3 and introduced a different notion of Balanced Arrays. Chatterjee and Mukerjee (1993) were the first who attempted to extend the two factor results to three factors They consider 2 × s2 × s3, s2 ≥ 2, s3 ≥ s2 factorial to derive D-optimal saturated main effect designs.
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