One-at-a-time designs

Two Experimental versus control subjects One-at-a-time designs Factorial designs Fractional factorial designs Nested designs Special designs... 

The table is not exhaustive, although it does include a majority of experimental designs that are used. One-at-a-time designs are the usual non-statistical type of experiments that are often carried out by scientists in all disciplines. Not included explicitly, however, are experimental designs that are generated from combinations of listed items. For example, a multi-factor experiment may have several levels of some of the factors but only two levels of other factors. 

An important purpose of a designed experiment is to obtain information about interactions among the primary variables. This is accompbshed by varying factors simultaneously rather than one at a time. Thus in Figure 2, each of the two preparations would be mn at both low and high temperatures using, for example, a full factorial experiment. 

A patented Dow-designed specimen bar magazine with a capacity of 125 bars makes the specimens available to the robotic arm. Specimens are stacked vertically, with their end tabs constrained by two channels so that only vertical motion is possible. A slot in the base of each channel allows the robot to pull specimens, one at a time, from the bottom of the stack. Once removed from the channels, the bars are dropped down a pair of circular slides which... 

Using experimental design such as Surface Response Method optimises the product formulation. This method is more satisfactory and effective than other methods such as classical one-at-a-time or mathematical methods because it can study many variables simultaneously with a low number of observations, saving time and costs [6]. Hence in this research, statistical experimental design or mixture design is used in this work in order to optimise the MUF resin formulation. 

This approach to heat exchanger network retrofit allows modifications to be introduced one at a time. In this way, the designer has control over the complexity of the network retrofit. At each stage, a suggested modification can be... 

The approach leads to simple and practical retrofit designs and has the major advantage that it allows the designer to assess modifications one at a time and to keep control over the complexity of the retrofit. Its disadvantage is that different combinations of modifications can be taken and there is no guarantee that this will lead to an optimum network retrofit. However, it is almost impossible to say that any retrofit is optimal or nonoptimal. The features of each retrofit are unique and it is difficult to formulate all the constraints for a retrofit in order to guarantee the very best retrofit. 

In the one-at-a-time procedure a change is made in a single variable and the results are evaluated. As this procedure is continued, a change in only one variable is made at each step along the way. This is well suited to plant design. 

For this last stage, the one-at-a-time procedure may be a very poor choice. At Union Carbide, use of the one-at-a-time method increased the yield in one plant from 80 to 83% in 3 years. When one of the techniques, to be discussed later, was used in just 15 runs the yield was increased to 94%. To see why this might happen, consider a plug flow reactor where the only variables that can be manipulated are temperature and pressure. A possible response surface for this reactor is given in Figure 14-1. The response is the yield, which is also the objective function. It is plotted as a function of the two independent variables, temperature and pressure. The designer does not know the response surface. Often all he knows is the yield at point A. He wants to determine the optimum yield. The only way he usually has to obtain more information is to pick some combinations of temperature and pressure and then have a laboratory or pilot plant experimentally determine the yields at those conditions. 

Thus, when statisticians got into the act, there saw a need to retain the information that was not included in the one-at-a-time plans, while still keeping the total number of experiments manageable the birth of statistical experimental designs . Several types of statistical experimental designs have been developed over the years, with, of course,... 

Because variables in models are often highly correlated, when experimental data are collected, the xrx matrix in Equation 2.9 can be badly conditioned (see Appendix A), and thus the estimates of the values of the coefficients in a model can have considerable associated uncertainty. The method of factorial experimental design forces the data to be orthogonal and avoids this problem. This method allows you to determine the relative importance of each input variable and thus to develop a parsimonious model, one that includes only the most important variables and effects. Factorial experiments also represent efficient experimentation. You systematically plan and conduct experiments in which all of the variables are changed simultaneously rather than one at a time, thus reducing the number of experiments needed. 

The confidence region obtained using a simulated one variable at a time design was first examined, since this was the design used by the original experimenters. 

Fig. 32. Approximate 95% confidence region for Eq. (149) and one variable at a time design.

Electrons do not fill orbitals one at a time. Nor do electrons have properties that designate individual electrons as first, second, third, fourth, etc. 

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