Experimental designs efficiency

A one-factor-at-a-time optimization is consistent with a commonly held belief that to determine the influence of one factor it is necessary to hold constant all other factors. This is an effective, although not necessarily an efficient, experimental design when the factors are independent. Two factors are considered independent when changing the level of one factor does not influence the effect of changing the other factor s level. Table 14.1 provides an example of two independent factors. When factor B is held at level Bi, changing factor A from level Ai to level A2 increases the response from 40 to 80 thus, the change in response, AR, is... 

W. J. Diamond, Practica/ Experimenta/ Designs for Engineers and Scientists, 2nd ed.. Van Nostrand Reinhold, New York, 1989. "This book is for engineers and scientists with Httie or no statistical background who want to learn to design efficient experiments and to analyze data correctiy. .. The emphasis is on practical methods, rather than on statistical theory." The discussion is quite detailed in some areas, eg, experimental designs based on Hadamard matrices, and scanty in others. 

Phase transfer catalysis has been used with success to prepare N- substituted pyrazoles (78MI40403, 79MI40408, 70JHC1237, 80JOC3172) and this procedure can be considered the simplest and most efficient way to obtain these compounds. Experimental design methodology has been used to study the influence of the factors on the reaction between pyrazole and -butyl bromide under phase transfer conditions (79MI40408). 

The effect of different pai ameters such as temperature, pressure, modifier volume, dynamic and static extraction time on the SFE of the plant were investigated. The orthogonal array experimental design method was chosen to determine experimental plan, (5 ). In this design the effect of five parameters and each at five levels were investigated on the extraction efficiency and selectivity [4]. 

Method development is important. LC-MS performance, probably more than any other technique involving organic mass spectrometry, is dependent upon a range of experimental parameters, the relationship between which is often complex. While it is possible (but not always so) that conditions may be chosen fairly readily to allow the analysis of simple mixtures to be carried out successfully, the widely variable ionization efficiency of compounds with differing structures often makes obtaining optimum performance for the study of all components of a complex mixture difficult. In such cases, the use of experimental design should be seriously considered. 

Increase efficiency of resource use, that is, obtain the desired information using the fewest possible necessary experiments (this is usually what is thought of when statistical experimental designs are considered). This aspect of experimentation is particularly important when the experiment is large to begin with, or if the experiment uses resources that are rare or expensive, or if the experiment is destructive, so that materials (especially expensive ones) are used up. 

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 ... 

Blunders must be eliminated, and all specified data must be collected. The efficiency of these experimental designs has another side effect any missing or defective data has a disproportionate effect relative to the amount of information that can be extracted from the final data set. When simpler experimental designs are used, where each piece of data is collected for the sole purpose of determining the effect of one variable, loss of that piece of data results in the loss of only that one result. When the more efficient statistical experimental designs are used, each piece of data contributes to more than one of the final results, thus each one is used the equivalent of many times and any missing piece of data causes the loss of all the results that are dependent upon it. 

This efficient statistical test requires the minimum data collection and analysis for the comparison of two methods. The experimental design for data collection has been shown graphically in Chapter 35 (Figure 35-2), with the numerical data for this test given in Table 38-1. Two methods are used to analyze two different samples, with approximately five replicate measurements per sample as shown graphically in the previously mentioned figure. 

Sections on matrix algebra, analytic geometry, experimental design, instrument and system calibration, noise, derivatives and their use in data analysis, linearity and nonlinearity are described. Collaborative laboratory studies, using ANOVA, testing for systematic error, ranking tests for collaborative studies, and efficient comparison of two analytical methods are included. Discussion on topics such as the limitations in analytical accuracy and brief introductions to the statistics of spectral searches and the chemometrics of imaging spectroscopy are included. 

Careful attention to quantitative activity vs. concentration relationships, to the effect of interaction terms in combinations (using computerized regression analysis and experimental design), and careful observation of the manner in which one mode of action supports and reinforces another, seems likely to lead us to the next generation of highly efficient flame retardant systems. 

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 goal of the four principles of experimental design is statistical efficiency and the economizing of resources.The single most important initial step in achieving such an outcome is to clearly define the objective of the study get a clear statement of what questions are being asked. 

The existence of a non-faradaic component to the overall current explains why the amount of material formed by electrochemical formation will generally be less than the theoretical amount, since the theoretical amount relates only to ffaradaic- Clearly, the coulometric efficiency should be maximized, i.e. /non-faradaic should be minimized by careful ehoice of experimental design, reagents and apparatus. Note that coulometric efficiency is also called faradaic efficiency. 

The experimental design in Figure 13.11 is more efficient than the experimental design in Figure 13.5 in the sense that fewer experiments are used to estimate the parameters of the model E = pif = 6/6 = l.(X)), but the quality of information (as... 

Tzeng et al studied the SCCO2 extractions with addition of 16.25% ethyl alcohol as a co-solvent to obtain scopoletin and artemisinin (1) from A. annua. A two-factor central composite experimental design was adopted to determine the optimal extraction conditions. Two-hour ethanol-modified SCCO2 extractions was more efficient than 16 h-Soxldet hexane extraction to provide pure artemisinin (1). ... 

In order to design efficient and stable reforming catalysts and to select the best operating conditions for hydrogen production, several experimental and theoretical studies have been performed using model compounds which are representative of the major classes of components present in bio-oils. 

The statistical techniques associated with response surface methodology are concerned primarily with two aspects of the experimentation process the construction of experimental designs that yield data to permit the efficient modeling of the response surfaces, and the analysis of the experimental data and derived response surfaces. 

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