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The purpose of this study is to fit an appropriate mathematical model to express response variables as functions of the proportions of the mixture components. One purpose of statistical modeling in a mixture experiment is to model the blending surface such that predictions of the response for any mixture component, singly or in combination, can be made empirically. Testing of the model adequacy will also be an important part of the statistical procedure.

A series of mortar using air lime, marble and ceramic sanitary waste aggregates were prepared for statistically designed combinations. The combinations were designed based on the mixture-design concept of design of experiments; this mortar is often used as a filler material in restoration projects. The aim of this work is to find an optimal composition of a paste for the manufacture of air lime mortar with ceramic and marble waste. This investigation aims to recommend mix design for air lime-based mortar, by optimizing the input combination for different properties, and to predict properties such as mechanical strength, thermogravimetric and x-ray diffraction analysis with a high degree of accuracy, based on a statistical analysis of experimental data.

This paper discusses those mortar properties that architects, contractors and owners consider important. For each of these properties, the influence of ceramic and marble waste in the air lime mortar is explored. The flexibility of lime-based mortars with waste materials to meet a wide range of needs in both new construction and restoration of masonry projects is demonstrated.

The objective of the present investigation is to recommend mixture design for air lime mortar with waste, by optimizing the input combination for different properties, and to predict properties such as compressive strength, flexural strength with a high degree of accuracy, based on the statistical analysis of experimental data. The authors conducted a mixture design study that takes into account dependent parameters such as the constituents of our air lime-based mortar where we have determined an experiment matrix to which we have connected the two responses, namely, compressive and flexural strength. By introducing the desirability criteria of these two responses, using JMP software, we were able to obtain a mixture optimal for air lime mortar with ceramic and marble waste.

The aim of this paper is to examine product formulation screening at the industrial level in terms of multi‐trait improvement by considering several pertinent controlling factors.

The study adopts Taguchi's orthogonal arrays (OAs) for sufficient and economical sampling in a mixture problem. Robustness of testing data is instilled in this method by employing a two‐stage analysis where controlling components are investigated together while the slack variable is tested independently. Multi‐responses collapse to a single master response has been incurred according to the Super Ranking concept. Order statistics are employed to provide statistical significance. The slack variable influence is tested by regression and nonparametric correlation.

Synergy among Taguchi methodology, super ranking and nonparametric testing was seamless to offer practical resolution to product component activeness. The concurrent modulation of two key product traits due to five constituents in the industrial production of muffin‐cake is invoked. The slack variable, rich cream, is strongly active while the influence of added amount of water is barely evident.

The method presented is suitable only for situations where industrial mixtures are investigated. The case study demonstrates prediction capabilities up to quadratic effects for five nominated effects. However, the statistical processor selected here may be adapted to any number of factor settings dictated by the OA sampling plan.

By using a case study from food engineering, the industrial production of a muffin‐cake is examined focusing on a total of five controlling mixture components and two responses. This demonstration emphasizes the dramatic savings in time and effort that are gained by the proposed method due to reduction of experimental effort while gaining on analysis robustness.

This work interconnects Taguchi methodology with powerful nonparametric tests of Kruskal‐Wallis for the difficult problem of non‐linear analysis of mixtures for saturated, unreplicated fractional factorial designs in search of multi‐factor activeness in multi‐response cases employing simple and practical tools.

The purpose of this work was to perform a systematic study on the effect of formulation on the physical and mechanical properties of ultaviolet (UV) curable urethane acrylate resins. In addition, the authors wanted to derive mathematical formula for the prediction of physical and mechanical properties for the aforementioned system.

The experiments were carried out based on mixture experimental design to determine the effect of different multifunctional acrylates (i.e. 1,6-hexanediol diacrylate (HDDA), tripropylene glycol diacrylate (TPGDA), trimethyolpropane triactylate (TMPTA)) concentration on the physical and mechanical properties of a UV curable polyurethane acrylate system. The urethane oligomer was synthesized and characterized by the research team. Microhardness, adhesion strength and scratch resistance of the cured films were evaluated as the physical and mechanical properties.

The results revealed that the resin and TMPTA concentrations had the most significant effects on the microhardness property. Adhesion strength of the films showed a linear trend with respect to all variables. Moreover, all components also had a significant and complex influence on the scratch resistance of the cured systems. In addition, mathematical equations proposed by mixture experimental design were derived for all the mentioned properties.

Other multifunctional acrylate monomers (i.e. more than three functional) can be used in the formulations. The kinetics of the curing can affect on the network formation and consequently on the properties of the cured films.

The obtained results can be used by the researchers who are active in the field of structure-property relationship of polymers and surface coatings. The reported data and the mathematical equations can also be used for the formulating of an appropriate formulation based on a specific application.

A systematic and statistical-based approach, i.e. mixture experimental design, was used to evaluate the effect of formulation on some of the properties of a UV curable polyurethane acrylate system. A urethane oligomer and three different multifunctional acrylate monomers as reactive diluents were used in the formulations. Noteworthy to mention that several mathematical models were derived by using analysis of variance for the prediction of the properties studied in this system.

The purpose of this study is to investigate and evaluate the impact of varying proportions of reinforcement on the mechanical properties of a modified Al₂O₃-LM6 cast composite under self-pouring temperature conditions. This study aims to determine the optimal mixture proportion of fine powders of Al, Si and xAl₂O₃ (with x values of 2%, 3% and 4%) through the application of design of experiment (DoE) and statistical analysis using the Minitab software. This study also involved evaluating the microstructural estimation and other physical properties of the cast composite to understand the combined effect of the reinforcement proportion on the material’s properties.

The researchers initially mixed the powders through ball milling and then compacted the moisture-free powder mix in a closed steel die. The resulting preforms were heated at the self-pouring temperature in an inert environment to fabricate the final cast composite. By applying DoE and performing an analysis of variance (ANOVA), the researchers sought to optimize the mixture proportion that would yield the best mechanical properties.

The experimental results indicated that a mixture combination of 83.5% Al blended with 12.5% Si and 4% Al₂O₃ led to the greatest improvement in mechanical properties, specifically in terms of increased density, hardness and impact strength. The ANOVA further supported the interaction effect of each processing parameter on the observed results. The results of this study offer valuable insights for the fabrication of modified Al₂O₃-LM6 cast composites under self-pouring temperature conditions. The identified optimal mixture proportion provides guidance for manufacturing processes and material selection to achieve improved mechanical properties in similar applications.

This study focuses on a specific composite material consisting of modified Al₂O₃ and LM6. Although Al₂O₃ and LM6 have been studied individually in various contexts, the combination of these materials and their impact on mechanical properties under self-pouring temperature conditions is a novel aspect of this research. The researchers use DoE methodology, along with statistical analysis using Minitab software, to optimize the mixture proportion and analyze the data. This systematic approach allows for a comprehensive exploration of the parameter space and the identification of significant factors that influence the mechanical properties of the composite.

The aim of this article is to demonstrate the development of environment friendly, low cost natural fibre composites by robust engineering approach. More specifically, the prime objective of the study is to optimise the composition of natural fibre reinforced polymer nanocomposites using a robust statistical approach.

In this research, the material is prepared using multi-walled carbon nanotubes (MWCNT), Cantala fibres and Epoxy Resin in accordance with the ASTM (American Society for Testing and Materials) standards. Further, the composition is prepared and optimised using the mixture-design approach for the flexural strength of the material.

The results of the study indicate that MWCNT plays a vital role in increasing the flexural strength of the composite. Moreover, it is observed that interactions between second order and third order parameters in the composition are statistically significant. This leads to proposing a special cubic model for the novel composite material with residual analysis. Moreover, the methodology assists in optimising the mixture component values to maximise the flexural strength of the novel composite material.

This article attempts to include both MWCNT and Cantala fibres to develop a novel composite material. In addition, it employs the mixture-design technique to optimise the composition and predict the model of the study in a step-by-step manner, which will act as a guideline for academicians and practitioners to optimise the material composition with specific reference to natural fibre reinforced nanocomposites.

Healthcare-associated infections (HAIs) are a major cause of concern because of the high levels of associated morbidity, mortality, and cost. In addition, children and intensive care unit (ICU) patients are more vulnerable to these infections due to low levels of immunity. Various medical interventions and statistical process control techniques have been suggested to counter the spread of these infections and aid early detection of an infection outbreak. Methods such as hand hygiene help in the prevention of HAIs and are well-documented in the literature. This chapter demonstrates the utilization of a systems methodology to model and validate factors that contribute to the risk of HAIs in a pediatric ICU. It proposes an approach that has three unique aspects: it studies the problem of HAIs as a whole by focusing on several HAIs instead of a single type, it projects the effects of interventions onto the general patient population using the system-level model, and it studies both medical and behavioral interventions and compares their effectiveness. This methodology uses a systems modeling framework that includes simulation, risk analysis, and statistical techniques for studying interventions to reduce the transmission likelihood of HAIs.

Jujube fruit (JF) (Ziziphus jujuba Mill.) is used as pharmaceuticals food, flavors and food additives. The purpose of this paper is to study the suitability of JF incorporation into a commercial sponge cake formulation, and to produce a nutritious bakery product with appropriate organoleptic and technological characteristics.

The optimal level of JF was incorporated into sponge cake using a custom mixture design with three independent variables, namely, refined wheat flour (RWF, 15–28 percent), sugar (7–22 percent) and JF (0–28 percent), as well as several responses, including physical properties, texture profile analysis (TPA), sensorial evaluation and color features. Moreover, physicochemical properties (TPA and oxidative indices) of optimal cake (two of the best JF levels) were compared with control sample (without JF) during 51 days storage period, while two baking temperatures (180°C and 170°C) were used.

The optimal amounts of RWF (21.19 percent), sugar (21.20 percent) and JF (7.61 percent) required for making the sample with maximum springiness, cohesiveness, specific volume, sensorial scores and yellowness, as well as the lowest firmness, baking loss and browning were determined. Desirable effects of JF on the cake quality well maintained throughout the storage period, as TPA attributes, peroxide value, ultraviolet absorbance and acid value showed less changes in JF-incorporated cake than the control sample.

Incorporating JF (~7 percent) into the batter was successful to improve the physicochemical properties in both fresh and stored cake with chocolate-like color.

The quality of probiotic yogurt which is remarked as a healthy, therapeutic and nutritious food product strongly depends on starter types and their compositions; however, the choice of starter culture affects the taste, aroma and quality of the final product. Through this study, to obtain favorable quality attributes of probiotic yogurt, a mixture of two thermophilic/mesophilic starter cultures (YC- 350/YC- X16) was applied for fermentation.

The effects of starter mixture, probiotic Lactobacillus paracasei and storage time on quality indices, such as apparent viscosity, water holding capacity, syneresis, post acidification rate and probiotic viability (L. paracasei), were assessed through using a combined (mixture-process) statistical design.

The results revealed that changes in viscosity and syneresis depend on the amount of YC- X16. Acidification rate was more pronounced at higher levels of YC- 350 (1.22 per cent) in comparison to that in YC-X16 (1.08 per cent) during storage time. With respect to probiotic viability, L. paracasei count was more than 107 cfu/mL during refrigerated storage time. Moreover, a promotive effect of YC- 350 on L. paracasei proliferation was observed in this study.

The favorable yogurt, from qualitative aspects, was manufactured at 75:25 per cent ratio of YC- X16:YC- 350 in probiotic type yogurts. Therefore, the use of mixed starter cultures developed textural properties of probiotic yogurt beside L. paracasei survival.

This paper aims to achieve phosphating via optimal features of Mg metal as a suitable base coating, which is considered for other properties such as barrier properties against the passage of several factors.

In this research, in the phosphate bath, immersion time, temperature and the content of sodium nitrite as an accelerator were changed.

As a result, increasing the immersion time of AZ31 Mg alloy samples in the phosphating bath as well as increasing the ratio of sodium dodecyl sulfate (SDS) concentration to sodium nitrite concentration in the phosphating bath formulation increase the mass of phosphating formed per unit area of the Mg alloy. The results of the scanning electron microscope test showed phosphating is not completely formed in short immersion times, which is a thin and uneven layer.

Mg and its alloys are sensitive to galvanic corrosion, which would lead to generating several holes in the metal. As such, it causes a decrease in mechanical stability as well as an unfavorable appearance.

Mg is used in several industries such as automobile and computer parts, mobile phones, astronaut compounds, sports goods and home appliances.

Nevertheless, Mg has high chemical reactivity, so an oxide-hydroxide layer is formed on its surface, which has a harmful effect on the adhesion and uniformity of the coating applied on Mg.

By increasing the ratio of SDS concentration to sodium nitrite concentration in the phosphating bath, the corrosion resistance of the phosphating increases.