Quality Improvement through Experiments with Mixtures

Mixture experiments are typical for chemical, food, metallurgical and other industries. The aim of these experiments is to find optimal component proportions that provide desired values of some product performance characteristics.

Experimental design on the simplex

Optimum experimental designs depend on the design criterion, the model and the design region. The talk will consider the design of experiments for regression models in which there is a single response with the explanatory variables lying in a simplex. One example is experiments on various compositions of glass such as those considered by Martin, Bursnall, and Stillman (2001). Because of the highly symmetric nature of the simplex, the class of models that are of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather different from those of standard regression analysis. The optimum designs are also rather different, inheriting a high degree of symmetry from the models. In the talk I will hope to discuss a variety of modes for such experiments. Then I will discuss constrained mixture experiments, when not all the simplex is available for experimentation. Other important aspects include mixture experiments with extra non-mixture factors and the blocking of mixture experiments. Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007). If time and my research allows, I would hope to finish with a few comments on design when the responses, rather than the explanatory variables, lie in a simplex. References Atkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum Experimental Designs, with SAS. Oxford: Oxford University Press. Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results on optimal and efficient designs for constrained mixture experiments. In A. C. Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000, pp. 225–239. Dordrecht: Kluwer. Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal Statistical Society, Ser. B 20, 344–360. 1

Aplicação da metodologia de planejamento de experimentos para formulação de massas cerâmicas para telhas

Rio Grande do Norte State stands out as one great producer of structural clay of the brazilian northeastern. The Valley Assu ceramic tiles production stands out obtained from ilitics ball clays that abound in the region under study. Ceramics formulation and the design of experiments with mixture approach, has been applied for researchers, come as an important aid to decrease the number of experiments necessary to the optimization. In this context, the objective of this work is to evaluate the effects of the formulation, temperature and heating rate in the physical-mechanical properties of the red ceramic body used for roofing tile fabrication of the Valley Assu, using design of mixture experiments. Four clays samples used in two ceramics industry of the region were use as raw material and characterized by X-ray diffraction, chemical composition, differential thermal analysis (DTA), thermogravimetric analysis (TGA), particle size distribution analysis and plasticity techniques. Afterwards, they were defined initial molded bodies and made specimens were then prepared by uniaxial pressing at 25 MPa before firing at 850, 950 and 1050 ºC in a laboratory furnace, with heating rate in the proportions of 5, 10 e 15 ºC/min. The following tecnologicals properties were evaluated: linear firing shrinkage, water absorption and flexural strength. Results show that the temperature 1050 ºC and heating rate of 5 ºC/min was the best condition, therefore presented significance in all physical-mechanical properties. The model was accepted as valid based of the production of three new formulations with fractions mass diferents of the initial molded bodies and heated with temperature at 1050 ºC and heating rate of 5 ºC/min. Considering the formulation, temperature and heating rate as variables of the equations, another model was suggested, where from the aplication of design of experiments with mixtures was possible to get a best formulation, whose experimental error is the minor in relation to the too much formulations

Regressão Simplex aplicada a delineamentos de mistura e utilização do Algoritmo Boosting

In the composition of this work are present two parts. The first part contains the theory used. The second part contains the two articles. The first article examines two models of the class of generalized linear models for analyzing a mixture experiment, which studied the effect of different diets consist of fat, carbohydrate, and fiber on tumor expression in mammary glands of female rats, given by the ratio mice that had tumor expression in a particular diet. Mixture experiments are characterized by having the effect of collinearity and smaller sample size. In this sense, assuming normality for the answer to be maximized or minimized may be inadequate. Given this fact, the main characteristics of logistic regression and simplex models are addressed. The models were compared by the criteria of selection of models AIC, BIC and ICOMP, simulated envelope charts for residuals of adjusted models, odds ratios graphics and their respective confidence intervals for each mixture component. It was concluded that first article that the simplex regression model showed better quality of fit and narrowest confidence intervals for odds ratio. The second article presents the model Boosted Simplex Regression, the boosting version of the simplex regression model, as an alternative to increase the precision of confidence intervals for the odds ratio for each mixture component. For this, we used the Monte Carlo method for the construction of confidence intervals. Moreover, it is presented in an innovative way the envelope simulated chart for residuals of the adjusted model via boosting algorithm. It was concluded that the Boosted Simplex Regression model was adjusted successfully and confidence intervals for the odds ratio were accurate and lightly more precise than the its maximum likelihood version.

Aplicação da metodologia de planejamento de experimentos para formulação de massas cerâmicas para telhas

Rio Grande do Norte State stands out as one great producer of structural clay of the brazilian northeastern. The Valley Assu ceramic tiles production stands out obtained from ilitics ball clays that abound in the region under study. Ceramics formulation and the design of experiments with mixture approach, has been applied for researchers, come as an important aid to decrease the number of experiments necessary to the optimization. In this context, the objective of this work is to evaluate the effects of the formulation, temperature and heating rate in the physical-mechanical properties of the red ceramic body used for roofing tile fabrication of the Valley Assu, using design of mixture experiments. Four clays samples used in two ceramics industry of the region were use as raw material and characterized by X-ray diffraction, chemical composition, differential thermal analysis (DTA), thermogravimetric analysis (TGA), particle size distribution analysis and plasticity techniques. Afterwards, they were defined initial molded bodies and made specimens were then prepared by uniaxial pressing at 25 MPa before firing at 850, 950 and 1050 ºC in a laboratory furnace, with heating rate in the proportions of 5, 10 e 15 ºC/min. The following tecnologicals properties were evaluated: linear firing shrinkage, water absorption and flexural strength. Results show that the temperature 1050 ºC and heating rate of 5 ºC/min was the best condition, therefore presented significance in all physical-mechanical properties. The model was accepted as valid based of the production of three new formulations with fractions mass diferents of the initial molded bodies and heated with temperature at 1050 ºC and heating rate of 5 ºC/min. Considering the formulation, temperature and heating rate as variables of the equations, another model was suggested, where from the aplication of design of experiments with mixtures was possible to get a best formulation, whose experimental error is the minor in relation to the too much formulations

Diffusion of Pure CH4 and Its Binary Mixture with CO2 in Faujasite NaY: A Combination of Neutron Scattering Experiments and Molecular Dynamics Simulations

The self-diffusion properties of pure CH4 and its binary mixture with CO2 within MY zeolite have been investigated by combining an experimental quasi-elastic neutron scattering (QENS) technique and classical Molecular dynamics simulations. The QENS measurements carried out at 200 K led to an unexpected self-diffusivity profile for Pure CH4 with the presence of a maximum for a loading of 32 CH4/unit cell, which was never observed before for the diffusion of apolar species in azeolite system With large windows. Molecular dynamics simulations were performed using two distinct microscopic models for representing the CH4/NaY interactions. Depending on the model, we are able to fairly reproduce either the magnitude or the profile of the self-diffusivity.Further analysis allowed LIS to provide some molecular insight into the diffusion mechanism in play. The QENS measurements report only a slight decrease of the self-diffusivity of CH4 in the presence of CO2 when the CO2 loading increases. Molecular dynamics simulations successfully capture this experimental trend and suggest a plausible microscopic diffusion mechanism in the case of this binary mixture.

Comparative productivity of irrigated short-term ryegrass (Lolium multiflorum) pasture receiving nitrogen, grown alone or in a mixture with white (Trifolium repens) and Persian (T. resupinatum) clovers

Dairy farms in subtropical Australia use irrigated, annually sown short-term ryegrass (Lolium multiflorum) or mixtures of short-term ryegrass and white (Trifolium repens) and Persian (shaftal) (T. resupinatum) clover during the winter-spring period in all-year-round milk production systems. A series of small plot cutting experiments was conducted in 3 dairying regions (tropical upland, north Queensland, and subtropical southeast Queensland and northern New South Wales) to determine the most effective rate and frequency of application of nitrogen (N) fertiliser. The experiments were not grazed, nor was harvested material returned to the plots, after sampling. Rates up to 100 kg N/ha.month (as urea or calcium ammonium nitrate) and up to 200 kg N/ha every 2 months (as urea) were applied to pure stands of ryegrass in 1991. In 1993 and 1994, urea, at rates up to 150 kg N/ha.month and to 200 kg N/ha every 2 months, was applied to pure stands of ryegrass; urea, at rates up to 50 kg N/ha.month, was also applied to ryegrass-clover mixtures. The results indicate that applications of 50-85 kg N/ha.month can be recommended for short-term ryegrass pastures throughout the subtropics and tropical uplands of eastern Australia, irrespective of soil type. At this rate, dry matter yields will reach about 90% of their potential, forage nitrogen concentration will be increased, there is minimal risk to stock from nitrate poisoning and there will be no substantial increase in soil N. The rate of N for ryegrass-clover pastures is slightly higher than for pure ryegrass but, at these rates, the clover component will be suppressed. However, increased ryegrass yields and higher forage nitrogen concentrations will compensate for the reduced clover component. At application rates up to 100 kg N/ha.month, build-up of NO3--N and NH4+-N in soil was generally restricted to the surface layers (0-20 cm) of the soil, but there was a substantial increase throughout the soil profile at 150 kg N/ha.month. The build-up of NO3--N and NH4+-N was greater and was found at lower rates on the lighter soil compared with heavy clays. Generally, most of the soil N was in the NO3--N form and most was in the top 20 cm.

The performance of irrigated mixtures of tall fescue, ryegrass and white clover in subtropical Australia. 1. The effects of sowing mixture combinations, nitrogen and oversowing on establishment, productivity, botanical composition and persistence.

In the subtropics of Australia, the ryegrass component of irrigated perennial ryegrass (Lolium perenne) - white clover (Trifolium repens) pastures declines by approximately 40% in the summer following establishment, being replaced by summer-active C4 grasses. Tall fescue (Festuca arundinacea) is more persistent than perennial ryegrass and might resist this invasion, although tall fescue does not compete vigorously as a seedling. This series of experiments investigated the influence of ryegrass and tall fescue genotype, sowing time and sowing mixture as a means of improving tall fescue establishment and the productivity and persistence of tall fescue, ryegrass and white clover-based mixtures in a subtropical environment. Tall fescue frequency at the end of the establishment year decreased as the number of companion species sown in the mixture increased. Neither sowing mixture combinations nor sowing rates influenced overall pasture yield (of around 14 t/ha) in the establishment year but had a significant effect on botanical composition and component yields. Perennial ryegrass was less competitive than short-rotation ryegrass, increasing first-year yields of tall fescue by 40% in one experiment and by 10% in another but total yield was unaffected. The higher establishment-year yield (3.5 t/ha) allowed Dovey tall fescue to compete more successfully with the remaining pasture components than Vulcan (1.4 t/ha). Sowing 2 ryegrass cultivars in the mixture reduced tall fescue yields by 30% compared with a single ryegrass (1.6 t/ha), although tall fescue alone achieved higher yields (7.1 t/ha). Component sowing rate had little influence on composition or yield. Oversowing the ryegrass component into a 6-week-old sward of tall fescue and white clover improved tall fescue, white clover and overall yields in the establishment year by 83, 17 and 11%, respectively, but reduced ryegrass yields by 40%. The inclusion of red (T. pratense) and Persian (T. resupinatum) clovers and chicory (Cichorium intybus) increased first-year yields by 25% but suppressed perennial grass and clover components. Yields were generally maintained at around 12 t/ha/yr in the second and third years, with tall fescue becoming dominant in all 3 experiments. The lower tall fescue seeding rate used in the first experiment resulted in tall fescue dominance in the second year following establishment, whereas in Experiments 2 and 3 dominance occurred by the end of the first year. Invasion by the C4 grasses was relatively minor (<10%) even in the third year. As ryegrass plants died, tall fescue and, to a lesser extent, white clover increased as a proportion of the total sward. Treatment effects continued into the second, but rarely the third, year and mostly affected the yield of one of the components rather than total cumulative yield. Once tall fescue became dominant, it was difficult to re-introduce other pasture components, even following removal of foliage and moderate renovation. Severe renovation (reducing the tall fescue population by at least 30%) seems a possible option for redressing this situation.

Theoretical and Computational Analysis of Static and Dynamic Anomalies in Water-DMSO Binary Mixture at Low DMSO Concentrations

Experiments have repeatedly observed both thermodynamic and dynamic anomalies in aqueous binary mixtures, surprisingly at low solute concentration. Examples of such binary mixtures include water-DMSO, water-ethanol, water-tertiary butyl alcohol (TBA), and water-dioxane, to name a few. The anomalies have often been attributed to the onset of a structural transition, whose nature, however, has been left rather unclear. Here we study the origin of such anomalies using large scale computer simulations and theoretical analysis in water-DMSO binary mixture. At very low DMSO concentration (below 10%), small aggregates of DMSO are solvated by water through the formation of DMSO-(H2O)(2) moieties. As the concentration is increased beyond 10-12% of DMSO, spanning clusters comprising the same moieties appear in the system. Those clusters are formed and stabilized not only through H-bonding but also through the association of CH3 groups of DMSO. We attribute the experimentally observed anomalies to a continuum percolation-like transition at DMSO concentration X-DMSO approximate to 12-15%. The largest cluster size of CH3-CH3 aggregation clearly indicates the formation of such percolating clusters. As a result, a significant slowing down is observed in the decay of associated rotational auto time correlation functions (of the S = O bond vector of DMSO and O-H bond vector of water). Markedly unusual behavior in the mean square fluctuation of total dipole moment again suggests a structural transition around the same concentration range. Furthermore, we map our findings to an interacting lattice model which substantiates the continuum percolation model as the reason for low concentration anomalies in binary mixtures where the solutes involved have both hydrophilic and hydrophobic moieties.

The gasification of wood-char spheres in CO2---N2 mixtures: analysis and experiments

The gasification of charcoal spheres in an atmosphere of carbon-dioxide-nitrogen mixture involving diffusion and reactions in the pores is modelled and the results are compared with experiments of Standish and Tanjung and those performed in the laboratory on wood-char spheres to determine the effects of diameter, density, gas composition and flow. The results indicate that the conversion time, t(c) approximately d1.03 for large particles (> 5 mm), departing substantially from the t(c) approximately d2 law valid for diffusion limited conditions. The computational studies indicate that the kinetic limit for the particle is below 100 mum. The conversion time varies inversely as the initial char density as expected in the model. Predictions from the model show that there is no significant change in conversion time up to 60% N2 consistent with the CO2-N2 experiments. The variation of diameter and density with time are predicted. The peculiar dependence of conversion time on flow velocity in the experiments is sought to be explained by opposing free and forced convection heat transfer and the attempt is only partly successful. The studies also indicate that the dependence on the CO concentration with low CO2 is significant, indicating the need for multistep reaction mechanism against the generally accepted single-step reaction.

Speeded up Gaussian mixture model algorithm for background subtraction

Adaptive Gaussian Mixture Models (GMM) have been one of the most popular and successful approaches to perform foreground segmentation on multimodal background scenes. However, the good accuracy of the GMM algorithm comes at a high computational cost. An improved GMM technique was proposed by Zivkovic to reduce computational cost by minimizing the number of modes adaptively. In this paper, we propose a modification to his adaptive GMM algorithm that further reduces execution time by replacing expensive floating point computations with low cost integer operations. To maintain accuracy, we derive a heuristic that computes periodic floating point updates for the GMM weight parameter using the value of an integer counter. Experiments show speedups in the range of 1.33 - 1.44 on standard video datasets where a large fraction of pixels are multimodal.

MULTI-INSTRUMENT DETECTION IN POLYPHONIC MUSIC USING GAUSSIAN MIXTURE BASED FACTORIAL HMM

We formulate the problem of detecting the constituent instruments in a polyphonic music piece as a joint decoding problem. From monophonic data, parametric Gaussian Mixture Hidden Markov Models (GM-HMM) are obtained for each instrument. We propose a method to use the above models in a factorial framework, termed as Factorial GM-HMM (F-GM-HMM). The states are jointly inferred to explain the evolution of each instrument in the mixture observation sequence. The dependencies are decoupled using variational inference technique. We show that the joint time evolution of all instruments' states can be captured using F-GM-HMM. We compare performance of proposed method with that of Student's-t mixture model (tMM) and GM-HMM in an existing latent variable framework. Experiments on two to five polyphony with 8 instrument models trained on the RWC dataset, tested on RWC and TRIOS datasets show that F-GM-HMM gives an advantage over the other considered models in segments containing co-occurring instruments.

Metal Retention Experiments for the Design of Soil-Mix Technology Permeable Reactive Barriers

Soil-mix technology is effective for the construction of permeable reactive barriers (PRBs) for in situ groundwater treatment. The objective of this study was to perform initial experiments for the design of soil-mix technology PRBs according to (i) sorption isotherm, (ii) reaction kinetics and (iii) mass balance of the contaminants. The four tested reactive systems were: (i) a granular zeolite (clinoptilolite-GZ), (ii) a granular organoclay (GO), (iii) a 1:1-mixture GZ and model sandy clayey soil and (iv) a 1:1:1-mixture of GZ, GO and model soil. The laboratory experiments consisted of batch tests (volume 900mL and sorbent mass 18g) with a multimetal solution of Pb, Cu, Zn, Cd and Ni. For the adsorption experiment, the initial concentrations ranged from 0.01 to 0.5mM (2.5 to 30mg/L). The maximum metal retention was measured in a batch test (300mg/L for each metal, volume 900mL, sorbent mass 90-4.5g). The reactive material efficiency order was found to be GZ>GZ-soil mix>GZ-soil-GO mix>GO. Langmuir isotherms modelled the adsorption, even in presence of a mixed cations solution. Adsorption was energetically favourable and spontaneous in all cases. Metals were removed according to the second order reaction kinetics; GZ and the 1:1-mix were very similar. The maximum retention capacity was 0.1-0.2mmol/g for Pb in the presence of clinoptilolite; for Cu, Zn, Cd and Ni, it was below 0.05mmol/g for the four reactive systems. Mixing granular zeolite, organoclay and model soil increased the chemisorption. Providing that GZ is reactive enough for the specific conditions, GZ can be mixed to obtain the required sorption. Granular clinoptilolite addition to soil is recommended for PRBs for metal contaminated groundwater. The laboratory experiments consisted of batch tests with a multimetal solution of Pb, Cu, Zn, Cd and Ni. The four reactive materials chosen were granular zeolite, clinoptilolite and model sandy clayey soil, granular organoclay and a mix of clinoptilolite, model soil and organoclay. The reactive material efficiency order was found to be granular clinoptilolite>clinoptilolite-soil mix>clinoptilolite-soil-organoclay mix>granular organoclay. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Transient state of chiral recognition in a binary mixture of cyclodextrins in capillary electrophoresis

The transient state (as the defined point where no enantioseparation is obtained in a dual chiral selector system) of chiral recognition of aminoglutethimide in a binary mixture of neutral cyclodextrins (CDs) was studied by capillary electrophoresis (CE). The following three dual selector systems were used: alpha-cyclodextrin (alpha-CD) and beta-cyclodextrin (beta-CD); alpha-CD and heptakis(di-O-methyl-beta-cyclodextrin) (DM-beta-CD); alpha-CD and heptakis(tri-O-methyl-beta-cyclodextrin) (TM-beta-CD). The S-(-) enantiomer of the analyte was more strongly retained in the presence of either alpha-CD or TM-beta-CD at pH 2.5, 100 mM phosphate buffer, while the R-(+) enantiomer was more strongly retained in the presence of either P-CD or DM-P-CD. In the more simple case, the elution order is invariably kept if the enantiomers have the same elution order in either one of the two hosts of the binary mixture. In contrast, the elution order may be switched by varying the concentration ratio of two hosts that produce opposite elution order for this particular analyte. In such a dual selector system, the enantioselectivity will disappear at the transient state at a certain ratio of host,:host, Moreover, the migration times of the two enantiomers with host, alone (diluted in buffer) is approximately equal to the migration times at the corresponding concentration of host, alone (diluted in buffer), where the ratio of concentrations of host,:host, is the same as in the binary mixture at the transient state. As found by nuclear magnetic resonance experiments, the analyte is forming a 1:1 complex with either one of the CDs applied. From this finding, a theoretical model based on the mobility difference of the two enantiomers was derived that was used to simulate the transient state. (C) 2000 Elsevier Science B.V. All rights reserved.

Rapid analysis of steroidal saponin mixture using electrospray ionization mass spectrometry combined with sequential tandem mass spectrometry

Using electrospray ionization mass spectrometry (MS) combined with sequential tandem MS(ESI-MSn), two major steroidal saponins extracted from Tribulus terrestris were studied, and considerable useful structural information was obtained. The structure of the proposed known steroidal saponin was verified, and the structure of the unknown saponin was investigated using MSn experiments. Some special fragment ions were also observed, and the corresponding fragmentation mechanisms were investigated which are characteristic for steroidal saponins and can give some information on the linkage position of some sugar groups in saponins. This methodology has been established as a powerful tool for the rapid, comparative analysis of mixtures such as crude plant extracts. (C) 1998 John Wiley & Sons, Ltd.