Sequential Design of Experiments

Too frequently, kinetic studies are deficient in their design. There is no fitting technique that can compensate for a poor experimental design. In the design of 

---

The sequential design of experiments and parameter estimation is covered in... 

Example 23,d.2-I Sequential Design of Experiments for Optimal Parameter Estimation in n-pentane Isomerization. Integral Method of Kinetic Analysis... 

Fig. 14 Confidence limits and criteria for the sequential design of experiments in parameter estimation.

For model discrimination and parameter estimation this reactor is part of a closed-loop-online microprocessor based computer system whose software structure is shown in Fig. 22. The three main program routines communicate via data files and a common part. This system can be operated interactively via a dialog routine and has implemented the above-mentioned criteria and numerical routines for the sequential design of experiments on model discrimination and... 

Procedures on how to make inferences on the parameters and the response variables are introduced in Chapter 11. The design of experiments has a direct impact on the quality of the estimated parameters and is presented in Chapter 12. The emphasis is on sequential experimental design for parameter estimation and for model discrimination. Recursive least squares estimation, used for on-line data analysis, is briefly covered in Chapter 13. 

J.J DiStefano III, Optimized blood sampling protocols and sequential design of kinetic experiments, Am. J. Physiol. 240 (1981) R259-R265. 

Design of Experiments Construction of efficient test patterns for these activities. Factorial designs are well treated by Box, Hunter, and Hunter (1978). Sequential procedures for experimental design are presented in Chapters 6 and 7 and Appendix C, and in the references cited there. 

If xi and X2 are varied one at a time, then the method is known as a univariate search and is the same as carrying out successive line searches. If the step length is determined so as to find the minimum with respect to the variable searched, then the calculation steps toward the optimum, as shown in Figure 1.15a. This method is simple to implement, but can be very slow to converge. Other direct methods include pattern searches such as the factorial designs used in statistical design of experiments (see, for example, Montgomery, 2001), the EVOP method (Box, 1957) and the sequential simplex method (Spendley et ah, 1962). 

In addition to aspects of early small-scale production, the development process itself can take advantage of MRT. It is interesting to note that already standardized microreaction systems are commercially available that allow sequential operations and, moreover, coupling to in-Hne analytical facilities [24]. Obviously, these devices are high-throughput tools for the combinatorial optimization of continuous reactions, e.g. the fully automated optimization of a reaction by the aid of DoE (Design of Experiments) can be reahzed within a few hours. 

The statistical analysis of data requires a proper design of experiments to prove or disprove a certain hypothesis which has been formulated in advance. From the viewpoint of a puritanical statistician most QSAR analyses are forbidden , because they are retrospective studies and, in addition, many different hypotheses (i.e. combinations of independent variables) are tested sequentially. Indeed, many problems arise from the application of regression analysis in ill-conditioned data sets. Only in later stages of lead structure optimization are certain hypotheses, e.g. on the influence of more lipophilic, electronegative, polar, or bulky substituents in a certain position, systematically tested, now fulfilling the requirements for the proper application of statistical methods. 

Figure 2.3J.2-2 Sequential procedure for optinud design of experiments from Froment [46]). 

Today a trend can be seen to computer aided experimentation. Not only the operation and control of the reactor but also automatic data sampling, analysis and statistically based sequential design of the experiments are performed by micro-computers /23,24,25/. In general, the experimental effort is appreciable and any method is welcome which can reduce the number of necessary experiments without loss of required accuracy. 

G.E.P. Box and H.L. Lucas Design of experiments in non-linear situations, Biometrika 46( 1959)77-90 /28/ L.H. Hosten A sequential experimental design procedure for precise parameter estimation based upon the shape of the joint confidence region, Chem.Eng.Sci. 29(1974)2247-2252... 

The first of these assumptions is the use of the Normal distribution. When we perform an experiment using a sequential design, we are implicitly using the experimentally determined value of s, the sample standard deviation, against which to compare the difference between the data and the hypothesis. As we have discussed previously, the use of the experimental value of s for the standard deviation, rather than the population value of a, means that we must use the f-distribution as the basis of our comparisons, rather than the Normal distribution. This, of course, causes a change in the critical value we must consider, especially at small values of n (which is where we want to be working, after all). 

---