Cross-classified designs

Finally, there are two families of factorial designs which depend on the combination mode of the factors. If it is possible to combine each level of one factor with each level of every other factor this is denoted cross-classified design. The second family consists of nested designs or hierarchical experiments. In those designs the levels of one factor may not be combined with all the levels of another factor. As an example consider an investigation performed by two laboratories (factor no. 1) which unfortunately cannot... 

This block design, in which each treatment appears once in each row and once in each column, is known as a Latin square. It allows the separation of the variation into the between-treatment, between-block, between-time-of-day and random experimental error components. More complex designs are possible which remove the constraint of equal numbers of blocks and treatments. If there are more than three blocks and treatments a number of Latin square designs are obviously possible (one can be chosen at random). Experimental designs of the types discussed so far are said to be cross-classified designs, as they provide for measurements for every possible combination of the factors. But in other cases (for example when samples are sent to different laboratories, and are analysed by two or more different experimenters in each laboratory) the designs are said to be nested or hierarchical, because the experimenters do not make measurements in laboratories other than their own. Mixtures between nested and cross-classified designs are also possible. 

There are various WT and FT boiler economizer designs, classified as either steaming economizer and nonsteaming economizer types according to thermal performance. These economizers are constructed in either bare tube or finned tube (extended surface) patterns. They may be positioned horizontally or vertically within the boiler system, in either cross-flow or counterflow arrangements. 

Catalytic reactors can roughly be classified as random and structured reactors. In random reactors, catalyst particles are located in a chaotic way in the reaction zone, no matter how carefully they are packed. It is not surprising that this results in a nonuniform fiow over the cross-section of the reaction zone, leading to a nonuniform access of reactants to the outer catalyst surface and, as a consequence, undesired concentration and temperature profiles. Not surprisingly, this leads, in general, to lower yield and selectivity. In structured reactors, the catalyst is of a well-defined spatial structure, which can be designed in more detail. The hydrodynamics can be simplified to essentially laminar, well-behaved uniform fiow, enabling full access of reactants to the catalytic surface at a low pressure drop. 

Mullin(3) has used this procedure for the design of a unit for the crystallisation of potassium sulphate at 293 K. The data are given in Table 15.5 from which it will be noted that the cross-sectional area depends linearly on the relative degree of de-supersaturation and the production rate depends linearly on the area but is independent of the height. If the production rate is fixed, then the crystalliser height may be adjusted by altering the sizes of the seed or product crystals. Mullin and Nyvlt(75) have proposed a similar procedure for mixed particle-size in a crystalliser fitted with a classifier at the product outlet which controls the minimum size of product crystals. 

Our study of the physical and coloration characteristics of 18th century silks has to be classified as an ideal study. We were able to closely examine a wide cross-section of textiles for all the clues that they contain. This type of cooperation involving the question of provenance, which is so difficult to determine for textiles because design migration and readaptation are so prevalent, has produced a systematic method for an approach to the documentation of 18th century Chinese and Western painted and printed silks (Tables I and II). 

Cross-flow trays are also classified according to the number of liquid passes on the plate. The design shown in Figure 11.23a is a single-pass plate. For low liquid flow... 

In this study, the automatic network designer was utilized for 10 parallel runs incorporating the same performance parameters as above. All of the 10 parallel performances proposed a 14 1 1 architecture. Each of the MLP ANN named modeling network in this work performed pattern recognition analysis with a 100% accuracy rate. In order to confirm the pattern recognition ability and the robustness of the proposed MLP ANN model, leave-one-out cross validation (40) was also carried out (i.e., the sample to be classified was deleted from the data set for the training of MLP ANN). The MLP ANNs... 

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