One-factor-at-a-time experiments

Empirical Modeling. The effect of process variables on the rate of depKJsition and properties of electrolessly depKJsited metals is usually studied by one-factor-at-a-time experiments (one-factor experiments are discussed further later in the book). In these experiments the effect of a single variable (factor), such as Xj, in the multivariable process with the response y, y = fixi, %2, X3,. .., x ), is studied by varying the value (level) of this variable while holding the values of the other independent variable fixed, y Any prediction (extrapolation) of the effect of a single variable on... 

DOE is an alternative to best-guess or one-factor-at-a-time experiments, which are time- and resource-intensive, and may not produce the optimal solution in the end. By using DOE to test more than one factor at a time, you ll end up with better, more reproducible solutions in less time, and you ll expend fewer resources. However, the approach does require rigorous statistical analysis and should only be used with support from statisticians or others who have been trained in DOE. 

Traditional one-factor-at-a-time experiments do not address interactions among product and process variables (7). 

In initial range-finding experiments, it is often practical to do one-factor-at-a-time experiments (4), followed by factorial screening designs using many factors (4,7), each at two levels. As we are interested in the properties of the concentration-response curve (particularly the difference between the asymptotes, the steepness of the responsive region, and the variation around the curve), it is important to quickly move to study the full curve. For cell-culture assays performed in 96-well plates, an effective approach is to assign... 

Factorial designs A factorial design is used to evaluate two or more factors simultaneously. The treatments are combinations of levels of the factors. The advantages of factorial designs over one-factor-at-a-time experiments are that they are more efficient and allow interactions to be detected. 

In a full factorial design all combinations between the different factors and the different levels are made. Suppose one has three factors (A,B,C) which will be tested at two levels (- and +). The possible combinations of these factor levels are shown in Table 3.5. Eight combinations can be made. In general, the total number of experiments in a two-level full factorial design is equal to 2 with /being the number of factors. The advantage of the full factorial design compared to the one-factor-at-a-time procedure is that not only the effect of the factors A, B and C (main effects) on the response can be calculated but also the interaction effects of the factors. The interaction effects that can be considered here are three two-factor interactions (AB,... 

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. 

Common practice consists in investigating the influence of one experimental variable (hereafter we will refer to it as a factor while keeping other factors at a fixed value. Then, another factor is selected and modified to perform the next set of experiments, and so forth. This one-factor-at-a-time strategy has been shown to be inefficient and expensive it lacks the ability to detect the joint influence of two or more factors (z.e. it cannot address interactions) and often needs many experiments. An increase in efficiency can be achieved by studying several factors simultaneously and systematically by means of an appropriate type of experimental design. In such a way, the experiments will be able to detect the influence of each factor and also the influence of two or more factors because every observation gives information about all factors. 

V. Czitrom, One-factor-at-a-time versus designed experiments. Am. Stat., 53(2), 1999, 126-131. 

Experiments may be designed to investigate one factor at a time so that all other independent variable-factors are held constant. This is the so-called classical experimental design. A classical experiment means researching mutual relationships between variables of a system, under "specially adapted conditions... 

TABLE 9.3. Experiment design for one-factor-at-a-time optimization (two-factor five-level). 

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. 

There are three ways scientists and engineers conduct controlled experiments success/failure, one-factor-at-a-time, and multiple factors at a time. Humans have used the first two since before recorded history, and still use them intuitively in many facets of our lives. In 1843, John S. Mill described these two approaches in his book Systems of Logic. He called... 

Design of experiments not only finds factors in complex processes that have a significant impact in their own right, but it can also find the joint interaction effects between these factors. The observational, success/failure, or one-factor-at-a-time approaches simply cannot find these interactions. When a process is described as more art than science, this usually suggests the joint interactions of factors that are not understood. The fact that those interactions are important is reinforced by the PMA Validation Advisory Committee ... 

Scientists and managers are traditionally taught that experiments should only change one factor at a time (e.g., temperature), holding other factors constant (time, pH, etc.). 

DOE is the only technique that enables scientists and managers to find, see, and use interaction effects that can improve product quality and yield or help set process boundaries to prevent failure. The well entrenched views that only one factor at a time can be studied and the widely held management maxim that if it ain t broke, don t fix it are not only wrong but, in some cases, dangerous a process can drift into failure, or periodically have an unexplainable failure, due to interaction effects. DOE permits scientists to conduct small scale, low cost process improvement experiments to model large scale, unbroken commercial processes without endangering current production runs and product supply. These same experiments can also generate data that drives continuous process improvement (read make more profitable ) of a process that ain t broke. ... 

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