Multistratum response surface designs

Response surface designs are usually described as if the treatments have been completely randomized to the experimental units. However, in practice there is often a structure to the units, implying the need for blocking. If, in addition, some factors are more difficult to vary between units than others, a multistratum structure arises naturally. We present a general strategy for constructing response surface designs in multistratum unit structures. Designs are constructed stratum by stratum, starting in the highest stratum. In each stratum a prespecified treatment set for the factors applied in that stratum is arranged to be nearly orthogonal to the units in the higher strata, allowing-for all the effects that have to be estimated. Three examples are given to show the applicability of the method and are also used to check the relationship of the final design to the choice of treatment set. Finally, some practical considerations in randomization are discussed.

An algorithm for arranging response surface designs in small blocks

We consider the problem of blocking response surface designs when the block sizes are prespecified to control variation efficiently and the treatment set is chosen independently of the block structure. We show how the loss of information due to blocking is related to scores defined by Mead and present an interchange algorithm based on scores to improve a given blocked design. Examples illustrating the performance of the algorithm are given and some comparisons with other designs are made. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Variance dispersion graphs for comparing blocked response surface designs

In this paper, we extend the use of the variance dispersion graph (VDG) to experiments in which the response surface (RS) design must be blocked. Through several examples we evaluate the prediction performances of RS designs in non-orthogonal block designs compared with the equivalent unblocked designs and orthogonally blocked designs. These examples illustrate that good prediction performance of designs in small blocks can be expected in practice. Most importantly, we show that the allocation of the treatment set to blocks can seriously affect the prediction properties of designs; thus, much care is needed in performing this allocation.

Some practical advice on polynomial regression analysis from blocked response surface designs

It is often necessary to run response surface designs in blocks. In this paper the analysis of data from such experiments, using polynomial regression models, is discussed. The definition and estimation of pure error in blocked designs are considered. It is recommended that pure error is estimated by assuming additive block and treatment effects, as this is more consistent with designs without blocking. The recovery of inter-block information using REML analysis is discussed, although it is shown that it has very little impact if thc design is nearly orthogonally blocked. Finally prediction from blocked designs is considered and it is shown that prediction of many quantities of interest is much simpler than prediction of the response itself.

Optimization of temperature, sugar concentration, and inoculum size to maximize ethanol production without significant decrease in yeast cell viability

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Row-column response surface designs

Factorial experiments are widely used in industry to investigate the effects of process factors on quality response variables. Many food processes, for example, are not only subject to variation between days, but also between different times of the day. Removing this variation using blocking factors leads to row-column designs. In this paper, an algorithm is described for constructing factorial row-column designs when the factors are quantitative, and the data are to be analysed by fitting a polynomial model. The row-column designs are constructed using an iterative interchange search, where interchanges that result in an improvement in the weighted mean of the efficiency factors corresponding to the parameters of interest are accepted. Some examples illustrating the performance of the algorithm are given.

Difference variance dispersion graphs for comparing response surface designs with applications in food technology

Variance dispersion graphs have become a popular tool in aiding the choice of a response surface design. Often differences in response from some particular point, such as the expected position of the optimum or standard operating conditions, are more important than the response itself. We describe two examples from food technology. In the first, an experiment was conducted to find the levels of three factors which optimized the yield of valuable products enzymatically synthesized from sugars and to discover how the yield changed as the levels of the factors were changed from the optimum. In the second example, an experiment was conducted on a mixing process for pastry dough to discover how three factors affected a number of properties of the pastry, with a view to using these factors to control the process. We introduce the difference variance dispersion graph (DVDG) to help in the choice of a design in these circumstances. The DVDG for blocked designs is developed and the examples are used to show how the DVDG can be used in practice. In both examples a design was chosen by using the DVDG, as well as other properties, and the experiments were conducted and produced results that were useful to the experimenters. In both cases the conclusions were drawn partly by comparing responses at different points on the response surface.

Modelagem e otimização por metodologia de superfícies de resposta: um estudo em arames de aço SAE 9254 para molas automobilísticas

Pós-graduação em Engenharia Mecânica - FEG

Optimization of fibrolytic enzyme production by Aspergillus japonicus C03 with potential application in ruminant feed and their effects on tropical forages hydrolysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Effect of soybean oil and Tween 80 on the production of botryosphaeran by Botryosphaeria rhodina MAMB-05

The addition of soybean oil and Tween 80 was evaluated with the objective of increasing the production of botryosphaeran, an exopolysaccharide (EPS) of the (1 -> 3 ;1 -> 6)-beta-D-glucan type produced by the fungus Botowsphaeria rhodina MAMB-05. Factorial design and analysis by response surface methodology was developed to select the main factors that would affect and enhance EPS production. The optimized culture conditions were: 40g l(-1) glucose with 10ml l(-1) soybean oil, and 4.5 ml l(-1) Tween 80, during 72h cultivation at 28 degrees C (180 rpm) and initial pH 5.7. The predicted result for botryosphaeran production was 8.22 +/- 1.36 g l(-1), and compared with the experimental value of 7.74 +/- 0.13 g l(-1) . Partial characterization of the botryosphaeran produced under the optimized conditions showed one type of polysaccharide with P-glycosidic linkages containing glucose as monosaccharide. (c) 2007 Elsevier Ltd. All rights reserved.

Botryosphaeran, a new substrate for the production of beta-1,3-glucanases by Botryosphaeria rhodina and Trichoderma harzianum Rifai

Botryosphaeria rhodina and Trichoderma harzianum Rifai were grown on botryosphaeran (an exopolysaccharide (EPS) of the beta-1,3; 1,6-D-Glucan type produced by B. rhodina) as sole carbon source with the objective of producing beta-glucanases of the beta-type. Conditions for beta-1,3-glucanase production by T harzianum were examined by a statistical response surface method, and showed maximal enzyme production at 5 days growth in media containing 1.5 g/1 of EPS. Good agreement was obtained between the experimental values of beta-1, 3-glucanase activity and the corresponding values predicted by the mathernatical model. The crude beta-1,3-glucanase preparations were active towards a number of different beta-1,3-glucans and beta-glucosides. The mycelium of B. rhodina also proved to be a good substrate for beta-1,3-glucanase production by both fungal species. (c) 2005 Published by Elsevier Ltd.

Efeito dos parâmetros de extrusão sobre as propriedades funcionais de extrusados da farinha de batata-doce

Farinha de batata-doce (Ipomoea batatas) foi extrusada em equipamento de rosca simples, mantendo-se fixas as temperaturas na 1ª e 2ª zonas de extrusão (20ºC e 60ºC, respectivamente). O efeito das variáveis umidade da farinha (15, 18 e 21%), temperatura na 3ª zona (100, 120 e 140ºC) e rotação da rosca (180, 210 e 240 rpm) sobre as características dos extrusados foi investigado utilizando-se metodologia de superfície de resposta. O teor de umidade e a temperatura de extrusão influenciaram significativamente a expansão dos extrusados. O índice de expansão apresentou valores crescentes com a temperatura sob baixos teores de umidade. A dureza dos extrusados e também o índice de absorção de água e o índice de solubilidade em água das farinhas extrusadas não mostraram modelo de regressão significativo com as condições de processo. Quanto à cor das farinhas, o componente L* (luminosidade) apresentou valores crescentes e o parâmetro a*, valores decrescentes com a elevação do teor de umidade até 20-21%. O parâmetro b* e a diferença de cor entre farinhas extrusadas e não extrusadas mostraram valores decrescentes com o aumento da umidade.

Efeitos de parâmetros de fermentação na produção de etanol a partir de resíduo líquido da industrialização da mandioca (manipueira)

Effect of fermentation parameters on ethanol production from cassava liquid residue (manipueira). "Manipueira", a liquid residue from the processing of cassava starch and flour, has recognized high pollution potential. Aiming at a possible use of "manipueira" as raw material for ethanol production, this study aimed to evaluate the effect of the percentage of inoculated yeast and fermentation temperature on the chromatographic profile of the components of wine of "manipueira". The residue was characterized for starch and sugar content, as well as pH and total acidity. The residue was hydrolyzed by the action of enzymes Termamyl 120 L and AMG 300 L. The hydrolysate obtained was fermented under different experimental conditions. A factorial central composite design (2(2)) with two independent variables and the response surface methodology were used to evaluate the results. The results showed a significant effect of variable parameters on the components of wine. The conditions of low fermentation temperature and lower percentages of inoculated yeast were the most appropriate to obtain ethanol from "manipueira".

Lactic acid production by new Lactobacillus plantarum LMISM6 grown in molasses: optimization of medium composition

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Improvement of L(+)-lactic acid production from cassava wastewater by Lactobacillus rhamnosus B 103

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)