Academic literature on the topic 'Complete factorial design'

In 2k complete factorial experiment, the experiment must be carried out in a completely randomized design. When the numbers of factors increase, the number of treatment combinations increase and it is not possible to accommodate all these treatment combinations in one homogeneous block. In this case, confounding in more than one incomplete block becomes necessary. In this paper, we considered the choice of confounding when k > 2. Our findings show that the choice of confounding depends on the number of factors, the number of blocks and their sizes. When two more interactions are to be confounded, their product module 2 should be considered and thereafter, a linear combination equation should be used in allocating the treatment effects in the principal block. Other contents in other blocks are generated by multiplication module 2 of the effects not in the principal block. Partial confounding is recommended for the interactions that cannot be confounded.

Efficiency and optimal properties of four varieties of Central Composite Design, namely, SCCD, RCCD, OCCD and FCCD and having r_f replicates of the full factorial portion, r_α replicates of the axial portion and r_c replicates of the center portion are studied in four to six design variables. Optimal combination,[r_f: r_α: r_c ] of design points associated with the three portions of each central composite design is presented. For SCCD, the optimal combinations resulting in A- and D- efficient designs generally put emphasis on replicating the center portion of the SCCD. However, replicating the center and axial portions allows for G-optimal and efficient designs. For RCCD, the optimal combinations resulting in A- and D- efficient designs generally put emphasis on replicating the factorial and center portions of the RCCD. However, replicating the center and axial portions allows for G-optimal and efficient designs. For OCCD, the optimal combinations resulting in A- optimal and efficient designs generally put emphasis on replicating the axial and center portion of the OCCD. The optimal combinations resulting in G- optimal and efficient designs generally put emphasis on replicating the factorial and axial portions of the OCCD. To achieve designs that are D-optimal and D-efficient, the optimal combination of design points generally put emphasis on replicating the center portion of the OCCD. For FCCD, the optimal combinations of design points resulting in A-efficient designs put emphasis on replicating the axial portion of the FCCD. The optimal combinations resulting in G- optimal and efficient designs as well as G-optimal and efficient designs generally put emphasis on replicating the factorial and axial portions of the FCCD. It is interesting to note that for FCCD in five design variables, any r^th complete replicate of the distinct design points of the combination [r_f: r_α: r_c ] resulted in a D-efficient design. Many super-efficient designs having efficiency values greater than 1.0 emerged under the D-criterion. Unfortunately, these designs did not perform very well under A- and G-criteria, having some efficiency values much below 0.5 or just about 0.6.

Abstract Bentonite clays are materials composed by one or more smectite clay minerals and some accessory minerals, mainly quartz, cristobalite, mica, feldspars and other clay minerals such as kaolinite. These contaminants present in clays have a large distribution of particle sizes which severely restrict their industrial applications, with the use of hydrocyclone as a likely solution for their reduction. This study aims to analyze the treatment of smectite clays from the state of Paraíba using modeling, simulation and optimization of the variable average particle diameter in relation to various process variables related to the hydrocyclone. In this study, the average diameter of smectite clays was evaluated as a function of the factors: pressure, apex diameter and vortex diameter of the hydrocyclone. Complete factorial design and addition in the central points were used to model the hydrocycloning process. The results evidenced reduction in equivalent average particle size of approximately 19.2%. Regarding the simulations, the optimum point with the lowest value was found for the average diameter of 4.033 µm, with a pressure of 4.3 bar, apex opening of 5.3 mm, and vortex opening of 6.3 mm, all at a 95% confidence level.