Optimal orthogonal block designs for a quadratic mixture model for three components

Depolymerization-liquefaction of plastics and rubbers. 2. Polystyrenes and styrene-butadiene copolymers

The use of gas jets (oxygen) plays a key role in several steelmaking processes as in the Basic Oxygen Furnace (BOF) or in the Electric Arc Furnace (EAF). Those jets improve heat, mass and momentum transfer in the liquid metal, mixing of chemical species enhancing and govern the formation of foaming slag. In this work experimental measurements were performed to determine the dimensions of the cavity formed at the liquid free surface caused by a gas jet impinging on it; also velocities vectors were measured in the zone affected by the gas jet. Cavities were measured from images from high speed camera and the vector maps were obtained with a Particle Image Velocimetry (PIV) technique. Both velocities and cavities were determined as a function of the main process variables: gas flow rate, distance of the nozzle from the free surface and lance angle. Cavity dimensions were statistically processed treated as a function of the process variables and also as a function of the proper dimensionless numbers that govern these phenomena. It was found thatWeber and Froude numbers govern the cavity geometry. Liquid flow driven by the jet is mainly affected by the air flow rate, lance height and angle.

The theory of optimal test-control block designs provides guidance on treatments allocation in experimental units. However, it is theoretically difficult to find them; therefore, the availability of an efficient and user-friendly algorithm for finding the optimal designs is essential for both researchers and practitioners. This paper describes an algorithm for constructing efficient test-control incomplete block designs with correlated observations. In order to evaluate the algorithm, we compare our results with the optimal designs presented in some published papers. An advantage of our algorithm is its independency to the size of blocks and the structure of correlation. Also, it takes to run between 30 s and 10 min depending on the type of CPU processor and the design.

In this paper a numerical method for construction of optimal Bayesian block designs of size two is considered. The main focus is on implementing prior information on the unknown error variance and variance of random block effects to calculate the A- and D-optimal designs. It is noted from the numerical results that the A- and D-optimal Bayesian block designs are insensitive to the shape of the prior distributions.

Consider a K-random factor design. Each random blocking factor,fk , has nk , levels and an allocation of the T fixed treatments under the consideration is applied to the experimental plots. In this paper the spectral representation of the covariance structure of such a design is given. Furthermore, the covariance structure under a mixed linear model which includes interactions between blocking factors and treatments is examined. As a result, we find that to preserve the covariance structure, not only does one need to impose conditions on the interactions but also to apply the treatments in a restricted fashion. We give a sufficient condition under which the structure of covariance of the model without interactions remains unchanged when interactions are included. That is to say that ANOVA for such designs based on the model without interactions remains valid when interactions actually do exist.

Pseudo-Bayesian [formula omitted]-optimal designs for estimating the point of maximum in component-amount Darroch–Waller mixture model

It is important to reduce metal losses associated with the slag in the blast furnace runner. Insufficient separation gives rise to technological problems in the subsequent processing of hot metal and slag in addition to the losses themselves. By using a water–oil physical model of the blast furnace trough, the flow behavior and the separation efficiency in the trough were investigated. A series of experiments was carried out by changing the process variables such as flow rate of liquids, properties of oil (slag), and geometrical design of the trough. The results indicate that, at constant physical properties, the flow velocity in the upper stream of the trough is the predominant factor in determining the amount of metal carried over with slag. Oil (slag) viscosity was also found to be an important contributor in the separation efficiency. The mechanism for the slag entrainment into the metal phase was also investigated. The results indicate that the amount of slag (oil) entrained into metal (water) is mainly determined by the force balance between inertial force in the metal stream, the viscous force, and the gravity force in the upper stream. Because of this mechanism, the oil entrainment ratio decreased sharply with oil volume while the effect of total flow rate, water and oil, was comparatively small. In order to extend the results obtained by this modeling study to the actual system, a technique of dimensional analysis was also employed. As a result, dimensionless group correlations which can describe the separation efficiency as a function of process variables and dimensions of the trough were derived.

Research is yet to be clone on the direct economy of the electro-discharge machining process which is a vital criterion for the users of the machine. In this paper an expression for contribution rate, as a function of process variables, which is a direct indicator to measure the economic objectives of the process for a production system is derived and a methodology forestimating the process and hence the objective function with respect to the process variables is cited. Further, in this paper a Complementary Geometric Programming algorithm is used to optimize the contribution rate under technical and technological constraints. This paper also compares the contribution rates obtained from the results of the optimization problem with the following objective functions under compatible sets of restrictions: (i) Contribution rate. (ii) Material removal rate. (iii) Electrode wear rate. (iv) Ratio of material removal rate to electrode wear rate. The data, for this paper is generated from JUSPA III, the electro-discharge machine based on the electronic pulse generator installed in the Machine Tool Research Laboratory at Jadavpur University, India.

Drying kinetics of four Fruits (namely, apple, pear, kiwi and banana) were studied by introducing an one-parameter empirical mass transfer model, involving a characteristic parameter (drying constant), as a function of process variables. The model was tested with data produced in a laboratory dryer, using non-linear regression analysis. The investigation involved a wide range of characteristic dimensions of samples and air conditions (temperature, humidity, and superficial velocity). The parameters of the model considered were found to be greatly affected by sample characteristic dimension and air temperature. The model also involved the equilibrium material moisture content which was formulated in the form of the GAB equation. Its parameters were evaluated by means of non-linear regression analysis to independent experiments covering two process variables (temperature and water activity of the surrounding air).

Enhancement of dimple formability in sheet metals by 2-step forming

Motivated by a question of C.-S. Cheng on optimal block designs, this paper describes the symmetric matrices with entries 0, +1 and −1, zero diagonal, least eigenvalue strictly greater than −2, and constant row sum. I also describe briefly the motivation for the question. Let A be a symmetric n× n matrix with entries 0, +1 and −1, with zero diagonal and constant row sums, having least eigenvalue greater than −2. The aim of this paper is to describe such matrices. Of course, we may assume that the matrix is “connected”, that is, not permutation-equivalent to one of the form ( B O O C ) . We also note that the constant row sum c is an eigenvalue, and so c ≥ −1. Such a matrix is represented by a set of vectors in a spherical root system, and hence (apart from finitely many examples represented in the exceptional root systems E6, E7 and E8) by either a tree with oriented edges, or a unicyclic graph with edges either signed or oriented. We give a test for recognising when such a graph represents a matrix satisying the conditions of the question. There are many examples. All matrices occurring in the exceptional root systems are determined. 1 Least eigenvalue −1 As a warmup, I consider the case where the least eigenvalue is −1.

On the optimality of a class of designs with three concurrences

In this article, we derive optimum designs for parameter estimation in a mixture experiment when the response function is linear in the mixing components with some synergistic effects. The D- and A-optimality criteria have been used for the purpose. The Equivalence Theorem has been used to check for the optimality of the proposed designs.

In response surface methodology, optimal designs are experimental designs generated based on a particular optimality criterion and are optimal only for a specific statistical model. Optimality criterion are single number criteria sometimes called alphabetical optimality criteria where each one intends to capture an aspect of the ‘goodness’ of a design. Most studies on optimization of process variables have concentrated on Central Composite Designs (CCD) yet second order rotatable deigns with any number of factors with reasonably small number of points constructed using properties of balanced incomplete block designs exist. A class of experimental designs that are optimal with respect to some statistical criterion are said to be Optimal designs. These designs allow parameter estimation with increased precision using fewer experimental runs, without bias and with minimum variance thus reducing time and costs of experimentation as opposed to non-optimal designs. A measure of relative efficiency of one design over another according to an optimality criterion aids in discriminating between the two designs for the “best” design. The D-, E-, A- and T-Optimal values of the general second order rotatable design in four dimensions constructed using balanced incomplete block designs when the number of replications (r) are less than three the number of times (λ) pairs of treatments occur together in the design were found which may be used to determine the relative efficiency of the general design to the D-, E-, A- and T-Optimal designs.

When fitting a response surface model, the least squares estimates of the model's parameters will generally depend on how the response surface design is blocked. Then, the choice of a blocking arrangement for a response surface design can have a considerable effect on estimating the mean response, on the size of the prediction variance and on the variance of the least squares estimator of the model's parameters. These are all shown to be affected by the sizes of the blocks and the allocation of experimental runs to the blocks. In this paper, we propose a graphical method for evaluating the effect of blocking in response surface designs. This graphical method can be used to examine how blocking influences the variance of the least squares estimator of the model's parameters. and to compare the effect of blocking in the cases of the orthogonal and nonorthogonal block designs, respectively