Quantitative Analysis of the Balance Property in Factorial Experimental Designs 24 to 28

Experimental designs are built by using orthogonal balanced matrices. Balance is a desirable property that allows for the correct estimation of factorial effects and prevents the identity column from aliasing with factorial effects. Although the balance property is well known by most researchers, the adverse effects caused by the lack or balance have not been extensively studied or quantified. This research proposes to quantify the effect of the lack of balance on model term estimation errors: type I error, type II error, and type I and II error as well as R2, R2adj, and R2pred statistics under four balance conditions and four noise conditions. The designs considered in this research include 24–28 factorial experiments. An algorithm was developed to unbalance these matrices while maintaining orthogonality for main effects, and the general balance metric was used to determine four balance levels. True models were generated, and a MATLAB program was developed; then a Monte Carlo simulation process was carried out. For each true model, 50,000 replications were performed, and percentages for model estimation errors and average values for statistics of interest were computed

Increase of <i>Trichoderma harzianum</i> Production Using Mixed-Level Fractional Factorial Design

This research presents the increase of the Trichoderma harzianum production process in a biotechnology company. The NOBA (Near-Orthogonal Balanced arrays) method was used to fractionate a mixed-level factorial design to minimize costs and experimentation times. Our objective is to determine the significant factors to maximize the production process of this fungus. The proposed 213242 mixed-level design involved five factors, including aeration, humidity, temperature, potential hydrogen (pH), and substrate; the response variable was spore production. The results of the statistical analysis showed that the type of substrate, the air supply, and the interaction of these two factors were significant. The maximization of spore production was achieved by using the breadfruit seed substrate and aeration, while it was shown that variations in pH, humidity, and temperature have no significant impact on the production levels of the fungus

One Note for Fractionation and Increase for Mixed-Level Designs When the Levels Are Not Multiple

Mixed-level designs have a wide application in the fields of medicine, science, and agriculture, being very useful for experiments where there are both, quantitative, and qualitative factors. Traditional construction methods often make use of complex programing specialized software and powerful computer equipment. This article is focused on a subgroup of these designs in which none of the factor levels are multiples of each other, which we have called pure asymmetrical arrays. For this subgroup we present two algorithms of zero computational cost: the first with capacity to build fractions of a desired size; and the second, a strategy to increase these fractions with M additional new runs determined by the experimenter; this is an advantage over the folding methods presented in the literature in which at least half of the initial runs are required. In both algorithms, the constructed fractions are comparable to those showed in the literature as the best in terms of balance and orthogonality

Alias Structures and Sequential Experimentation for Mixed-Level Designs

Alias structures for two-level fractional designs are commonly used to describe the correlations between different terms. The concept of alias structures can be extended to other types of designs such as fractional mixed-level designs. This paper proposes an algorithm that uses the Pearson’s correlation coefficient and the correlation matrix to construct alias structures for these designs, which can help experimenters to more easily visualize which terms are correlated (or confounded) in the mixed-level fraction and constitute the basis for efficient sequential experimentation

Alias Structures and Sequential Experimentation for Mixed-Level Designs

Alias structures for two-level fractional designs are commonly used to describe the correlations between different terms. The concept of alias structures can be extended to other types of designs such as fractional mixed-level designs. This paper proposes an algorithm that uses the Pearson&rsquo;s correlation coefficient and the correlation matrix to construct alias structures for these designs, which can help experimenters to more easily visualize which terms are correlated (or confounded) in the mixed-level fraction and constitute the basis for efficient sequential experimentation