Planning experiments experimental design

Planning experiments statistically—design of experiments (DOE)—is not only driven by economic issues but also by the need to derive the correct (unique) solution. Running experiments is time consuming and/or expensive and thus it becomes imperative to minimize their number while maximizing the information generated. Various experimental methodologies have been... 

Experimental design can be used for optimization purposes where the optimum may be the highest or lowest value of the responses or simply a region where the results are sufficiently go. The word design means that the experiments are not carried out in a haphazard way, but in a carefully considered and planned way. Experimental designs are applied to obtain not only optimal responses but also optimal models, i.e., in calibration. 

Such programs generally concentrate on the technical parts of designing an experiment, and provide limited guidance on the important, softer aspects of experimental design stressed in this article. Also, most computer routines do not allow one to handle various advanced concepts that arise frequently in practice, eg, spHt plot and nested situations, discussed in the books in the bibhography. In fact, some of the most successful experiments do not involve standard canned plans, but are tailored to fit the problem at hand. 

C. Daniel, App/ications of Statistics to lndustria/Experimentation, ]oE Wiley Sons, Inc., New York, 1976. This book is based on the personal experiences and insights of the author, an eminent practitioner of industrial appHcations of experimental design. It provides extensive discussions and concepts, especially in the areas of factorial and fractional factorial designs. "The book should be of use to experimenters who have some knowledge of elementary statistics and to statisticians who want simple explanations, detailed examples, and a documentation of the variety of outcomes that may be encountered." Some of the unusual features are chapters on "Sequences of fractional repHcates" and "Trend-robust plans," and sections entided, "What is the answer (what is the question )," and "Conclusions and apologies."... 

This technique is readily adaptable for use with the generalized additive physical approach discussed in Section 3.3.3.2. It is applicable to systems that give apparent first-order rate constants. These include not only simple first-order irreversible reactions but also irreversible first-order reactions in parallel and reversible reactions that are first-order in both the forward and reverse directions. The technique provides an example of the advantages that can be obtained by careful planning of kinetics experiments instead of allowing the experimental design to be dictated entirely by laboratory convention and experimental convenience. 

The key to all statistical experimental designs is planning. A properly planned experiment can achieve all the goals set forth above, and in fewer runs than you might expect (that s where achieving the goal of efficiency comes in). However, there are certain requirements that must be met ... 

These types of experimental designs also have some limitations. The first is the exaggeration of the effect of missing or defective data on the results, as mentioned above. The second is the fact that until the entire plan is carried out, little or no information can be obtained. There are generally few, if any, intermediate results only after all the data is available can any results at all be calculated, and then all of them are calculated at once. This phenomenon is related to the first caveat until each piece of data is collected, it is missing from the experiment, and therefore the results that depend upon it cannot be calculated. 

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. 

Eor every microarray experiment the first and most important step is experimental design. A badly designed experiment can render microarray data unsuitable for addressing the experimental questions or worse, lead the investigator to draw false conclusions. Furthermore, failed microarray experiments can be very costly both in terms of resources and time. There are many issues that must be addressed when planning a cDNA microarray experiment, some intuitive, others requiring considerable thought. 

Ghosh, S., Ed. (1990), Statistical Design and Analysis of Industrial Experiments, Dekker, New York, NY. Gibson, R.J. (1968), Experimental Design, or Happiness is Planning the Experiment, Bioscience, 18,223-225. Gitlow, H., Gitlow, S., Oppenheim, A., and Oppenheim, R. (1989), Tools and Methods for the Improvement of Quality, Irwin, Homewood, IL. 

Study means an experiment or set of experiments in which a test item is examined. The study plan defines the objectives and experimental design of the study. 

Initial screens can be distinguished between methods that are used to determine what factors are most important, and follow-up screens that allow optimization and improvement of crystal quality (Table 14.1). In experimental design, this is known as the Box-Wilson strategy (Box et al., 1978). The first group of screens is generally based on a so-called factorial plan which determines the polynomial coefficients of a function with k variables (factors) fitted to the response surface. It can be shown that the number of necessary experiments n increases with 2 if all interactions are taken into account. Instead of running an unrealistic, large number of initial experiments, the full factorial matrix can... 

In the simultaneous approach the experiments are planned beforehand (preferably using experimental design techniques) and performed randomly. With RSM techniques the obtained experimental data can be used to model the quality criterion as a function of the design variables. Then an optimal setting of the design variables can be calculated. All the optimization experiments described in this book are using the simultaneous approach. The simultaneous approach uses in almost all... 

An excellent exposition of split-plot experimental designs can be found in D.R. Cox s book, Planning of Experiments [42]. He states that split-plot designs are particularly useful when one (or more) factors are what he calls classification factors. These factors are included in the experiment to determine whether they modify the effect of the other factors or indicate how the other factors work. The classification factors are included to examine their possible interaction with the other factors. Lower precision is tolerated for comparisons of the classification factors, in order that the precision of the other factors and the interactions can be increased. In the standard terminology associated with split-plot experiments, the classification factors are called whole-plot factors and are applied to the larger experimental units. The smaller experimental units are called subplots. 

How and why the response is fitted to these models is discussed later in this chapter. Note here that the coefficients (3 represent how much the particular factor affects the response the greater (3i, for example, the more Nchanges as R changes. A negative coefficient indicates that N decreases as the factor increases, and a value of zero indicates that the factor has no effect on the response. Once the values of the factor coefficients are known, then, as with the properly modeled systems, mathematics can tell us the position of the optimum and give an estimate of the value of the response at this point without doing further experiments. Another aspect of experimental design is that, once the equation is chosen, an appropriate number of experiments is done to ascertain the values of the coefficients and the appropriateness of the model. This number of experiments should be determined in advance, so the method developer can plan his or her work. 

If an experiment has been properly designed or planned, the data will be collected in the most efficient form for the problem being considered. Experimental design is the sequence of steps initially taken to insure that the data will be obtained in such a way that its analysis will lead immediately to valid statistical inferences. Before a design can be chosen, the following questions must be answered ... 

The challenge here is experimental design. Scientists from the more experimental disciplines will probably already be aware of the need for design when planning an experiment, but it may not be obvious that the successful construction of QSAR models also calls for experimental design. Each compound tested or included in a QSAR analysis corresponds to a design point the experimental... 

This section deals with interpretive optimization methods. In these. methods, the extent of chromatographic separation is predicted indirectly from the retention behaviour of the individual solutes. The data are interpreted to locate the optimum in terms of the complete chromatogram. The interpretive methods may involve a limited number of experiments according to a pre-planned experimental design (section 5.5.1) or may start with a minimum number of experiments in order to try and locate the optimum by an iterative process (section 5.5.2). 

In this section we will describe several optimization procedures which are simultaneous in the sense that all experiments are performed according to a pre-planned experimental design. However, unlike the methods described in section 5.2, the experimental data are now interpreted in terms of the individual retention surfaces for all solutes. The window diagram is the best known example of this kind of procedure. 

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