One Factor at a Time method

Third, there is the one-factor-at-a-time method in which the experimenter varies first one factor to find the best value, then another. Its disadvantages are that it cannot be used for multiple responses and that it will not work when there are strong interactions between factors. 

Figure 22.4 The one factor at a time method. If there is a surface of continuous response, the iso-response curves have will lead to a variety of optimum situations.

The one-factor-at-a-time method (which is in itself an experimental design) is inefficient, can give misleading results, and in general it should be avoided. In the vast majority of cases our approach will be to vary all factors together. 

The influence of each factor on the yield of pellets is estimated with a far higher precision than by changing the factors one at a time. In fact, the standard error of estimation is halved. To obtain the same precision by the one-factor-at-a-time method each experiment would have to be done 4 times. 

The number of experiments is the same as for the one-factor-at-a-time method. 

Why do chemists run their experiments mostly by one-factor-at-a-time methods ... 

Secondly, with the OVAT approach the importance of interactions is not taken into account. An interaction between two factors is present when the effect of one factor depends on the level of another factor. Since only one factor at a time is varied, the presence or absence of interactions cannot be verified. However, this is not dramatic, since in robustness testing the interaction effects are considered negligible. The evaluation of such interactions is more important in method optimization. 

In the optimization of tablet formulations, different approaches can be used. The one variable at a time method requires many experiments and there is no guarantee that an optimal formulation is achieved. Moreover the interaction between different factors, which may influence the tablet properties, will not be detected [10]. The use of an experimental design can be helpful in the optimization of tablet formulations. Mixture designs can be used to describe the response (tablet properties) as a function of the... 

For determining the robustness of a method a number of parameters, such as extraction time, mobile-phase pH, mobile-phase composition, injection volume, source of column lots and/or suppliers, temperature, detection wavelength, and the flow rate, are varied within a realistic range and tlie quantitative influence of the variables is determined. If the influence of a parameter is within a previously specified tolerance, this parameter is said to be witliin the robustness range of the method. These method parameters may be evaluated one factor at a time or simultaneously as part of a factorial experiment. 

Knowledge of multivariate methods is not, however, widely spread in the community of synthesis chemists. Therefore, many new methods are still being investigated through poorly designed experiments and hence, new procedures are not properly optimized. Still, the most common method to carry out "systematic studies" is to consider "one factor at a time", although such an approach was shown by R.A. Fisher to be inappropriate over 60 years ago [1], when several factors are to be considered. 

If the factors involved in an analysis are independent (which is rarely the situation), a common practice is to experiment with one factor at a time while holding all others fixed, then the influence of each one can be studied on the result by using a simple repetitive method. 

It is also possible to use the factor label method to convert from one ratio to an equivalent ratio, using one factor at a time. 

When the optimum is outside the domain, we need to arrive at it rapidly. Changing one factor at a time will not work well, especially if there are interactions. One possibility is to use the sequential simplex, but it is here also that the steepest ascent method comes into its own. The procedure is simple. Assuming that the response (such as the yield) is to be maximized, we determine this response as a function of the coded variables x, x, . .. and find the position and direction of maximum rate of increase (steepest ascent) in terms of these coded variables. 

In this chapter, we begin with an introduction to DoE in Section 8.1. In Section 8.2, we discuss the One Factor At A Time approach which is generally used among scientists and engineers. In Section 8.3, we consider traditional methods implemented in nanotechnology experimentation in practice. Next, in Section 8.4, we propose... 

The practice of estabHshing empirical equations has provided useflil information, but also exhibits some deficiencies. Eor example, a single spray parameter, such as may not be the only parameter that characterizes the performance of a spray system. The effect of cross-correlations or interactions between variables has received scant attention. Using the approach of varying one parameter at a time to develop correlations cannot completely reveal the tme physics of compHcated spray phenomena. Hence, methods employing the statistical design of experiments must be utilized to investigate multiple factors simultaneously. 

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