Tutorial for mixture-process experiments with an industrial application

Bello, Luiz Henrique Abreu Dal; Vieira, Antonio Fernando de Castro

doi:10.1590/s0101-74382011000300008

Cited by 7 publications

(9 citation statements)

References 19 publications

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“…Different mathematical models are utilized to analyze data in the mixture experiment as suggested by Scheffe's model (Cornell, ). The canonical or Scheffe's models are as follows (Bello & Castro Vierira, ):

Linear : Q (y) = {false\sum}_{i = 1}^{q} {normalβ}_{i} X_{i}

Quadratic : Q (y) = {false\sum}_{i = 1}^{q} {normalβ}_{i} X_{i} + {false\sum}_{1 \leq i < j}^{q} {normalβ}_{i j} X_{i} X_{j}

Special cubic : Q (y) = {false\sum}_{i = 1}^{q} {normalβ}_{i} X_{i} + {false\sum}_{1 \leq i < j}^{q} {normalβ}_{i j} X_{i} X_{j} + {false\sum}_{1 \leq i < j < k}^{q} {normalβ}_{i j} X_{i} X_{j} X_{k}

\begin{matrix} Full cubic : Q (y) = & {false\sum}_{i = 1}^{q} {normalβ}_{i} X_{i} + {false\sum}_{1 \leq i < j}^{q} {normalβ}_{i j} X_{i} X_{j} + \sum {normalγ}_{i j} X_{i} X_{j} (X_{i} - X_{j}) \\ + false\sum 1 \leq i < j \end{matrix}

…”

Section: Methodsmentioning

confidence: 99%

Effect of high‐amylose corn starch addition on canning of yellow alkaline noodle composed of wheat flour and microbial transglutaminase: Optimization by RSM

Mojarrad¹,

Rafe²

2018

Food Science & Nutrition

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Mixture experiment was applied to optimize the canned cross‐linked high‐amylose starch yellow alkaline noodle formula. Processing factors of canned yellow alkaline noodle (YAN) cross‐linked by MTGase at different levels of Hylon VII were surveyed. The factors were wheat flour, Hylon VII starch (HAS) as a high‐amylose starch, and water in the mixture to achieve reduction in cooking loss, water uptake, swelling index, and thickness. Due to the effect of retort processing on YAN, pH, color, and texture were also examined. Analysis of variance showed that the linear mixture had a significant effect on the noodle properties. Optimum conditions were as follows: wheat flour of 75 g, HAS of 15 g, and water 67 ml. Results showed the suitable effect of Hylon in improving texture of canned YAN as well as high gel strength, neutral pH, lowest cooking loss, water uptake, swelling index, and color after retort processing. Therefore, high‐amylose decreased swelling of starch, cooking yield, and improved hardness which obtain a strong gel and better stability in canned noodle. The pH fall and the attainment of yellow color in the YAN containing Hylon can be explained by the availability of two important amino acids, lysine and glutamine which were involved in both cross‐linking reactions. The synergistic effect of low amount of flour and Hylon produced more tensile and hardness properties in canned noodle. Overall, the canned YAN prepared by adding Hylon developed the stronger gel which can withstand at high thermal retort processing and finally improve the shelf life of the final product.

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Linear : Q (y) = {false\sum}_{i = 1}^{q} {normalβ}_{i} X_{i}

Quadratic : Q (y) = {false\sum}_{i = 1}^{q} {normalβ}_{i} X_{i} + {false\sum}_{1 \leq i < j}^{q} {normalβ}_{i j} X_{i} X_{j}

Special cubic : Q (y) = {false\sum}_{i = 1}^{q} {normalβ}_{i} X_{i} + {false\sum}_{1 \leq i < j}^{q} {normalβ}_{i j} X_{i} X_{j} + {false\sum}_{1 \leq i < j < k}^{q} {normalβ}_{i j} X_{i} X_{j} X_{k}

\begin{matrix} Full cubic : Q (y) = & {false\sum}_{i = 1}^{q} {normalβ}_{i} X_{i} + {false\sum}_{1 \leq i < j}^{q} {normalβ}_{i j} X_{i} X_{j} + \sum {normalγ}_{i j} X_{i} X_{j} (X_{i} - X_{j}) \\ + false\sum 1 \leq i < j \end{matrix}

…”

Section: Methodsmentioning

confidence: 99%

Effect of high‐amylose corn starch addition on canning of yellow alkaline noodle composed of wheat flour and microbial transglutaminase: Optimization by RSM

Mojarrad¹,

Rafe²

2018

Food Science & Nutrition

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“…The main effects (X1, X2, X3 and X4) represent the average result of modifying a factor. The interaction terms (X1X4, X2X3, X2X4, X2X4 and X3X4) show how the response changes when two or more factors are modi ied simultaneously (Cornell, 2011;Tinsson, 2010;Tabandeh and Erfan, 2013;Bello et al, 2011).…”

Section: Development Of Mathematical Modelsmentioning

confidence: 99%

“…Figure 1 represent the degree of reconciliation of the experimental data with the data predicted by the model. The model allowed a better adjustment of the data (Dabbas et al, 2003;Bello et al, 2011).…”

Section: Statistical Modelingmentioning

confidence: 99%

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Application of design mixture and desirability function in the optimization of pharmaco-technical parameters of macrogols-based suppositories

Benomar

Yanisse

Charkaoui

et al. 2020

ijrps

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The objective of this work is to (i) study the effect of variations in the proportions of four Macrogols on the pharmaco-technical characteristics of suppositories, (ii) define the optimal formula for a suppository with immediate effect; maximum disintegration and a minimum of hardness as defined in the European Pharmacopoeia. The lattice design mixture has been proposed as an optimization technique, the formulation factors are presented by the proportions of PEG 400 (X1), PEG 600 (X2), PEG 4000 (X3) and PEG 6000 (X4) and the response variables are (i) the disintegration time (Y1) (ii) the hardness (Y2). The second-degree empirical model was postulated to model the variations of the two response variables using the least-squares method. The selected model explained about 67% and 84% of the variation for Y1 and Y2, respectively. All four factors had significant effects on the properties of the suppository. Interactions negatively affected both responses. The numerical desirability method gave the following optimal formula: PEG400 (28.71334 %); PEG600 (24.23773%), PEG4000 (35.00944%) and PEG6000 (12.03949%) for a disintegration of 25.839 (+/-2.3) min and hardness =2147.321 (+/- 50) g.

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“…In this paper, we have extended our previous work (Habib & Marimuthu, 2016;Habib & Marimuthu, 2017) on an analytical modelling of data trust by exploring the trustworthiness through an intelligent-transparent-trust triangulation model, in which we have defined a trust triangle analogous to an opinion triangle (Dal Bello & Vieira, 2011;Jøsong, 2008). We have considered three parameters, namely, intelligence, transparency, and untrustworthiness, as the vertices of an equilateral triangle, and we have derived a new set of relations depicting the possible misbehaviours.…”

mentioning

confidence: 98%

Analysis of data trust through an intelligent–transparent–trust triangulation model

Habib

Marimuthu

2018

Expert Systems

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Computing sensor systems are involved in making vital decisions based on sensed data. Thus, the data need to be trustworthy. We have made a novel attempt to analyse the trustworthiness of computing sensor systems outcomes by modelling trust as an association triangle between intelligence, transparency, and trust. Intelligence represents the computing algorithm, which makes the vital decisions, and transparency represents completeness by explicitly specifying the decision‐making process. We propose a triangulation model as a framework for assessing the trust, and we have selected 2 trust factors analogous to transparency and intelligence: the deviation of malfunctioning sensor data from its neighbours and the deviation from its own history. We have derived a set of relationships between the trust factors and their outcomes, and we have associated them with the proposed triangulation model. We also have formulated the generation of a trust subspace as an optimization problem with an objective function to maximize the trust. We have employed Tabu Search combined with Simulated Annealing to search for the best possible weighted combinations of trust factors. We have projected the experimental results onto a 3‐coordinate equilateral triangle to validate the decision analysis by displaying a definite trust or untrustworthiness of data.

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Tutorial for mixture-process experiments with an industrial application

Cited by 7 publications

References 19 publications

Effect of high‐amylose corn starch addition on canning of yellow alkaline noodle composed of wheat flour and microbial transglutaminase: Optimization by RSM

Effect of high‐amylose corn starch addition on canning of yellow alkaline noodle composed of wheat flour and microbial transglutaminase: Optimization by RSM

Application of design mixture and desirability function in the optimization of pharmaco-technical parameters of macrogols-based suppositories

Analysis of data trust through an intelligent–transparent–trust triangulation model

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