Application of statistical experimental

Application of Statistical Experimental Design to Development of Low-Density Polymer Foams... 

This chapter will examine the application of statistical experimental design to designing a product or process that is robust to variation from environmental variables. It should be understood that the phrase environmental variables is to be viewed broadly and is not just limited to variables such as temperature and humidity. In this context, variation from environmental variables is variation that is external to the product and that is outside of the control of the manufacturer during production. Thus, it might also include variation in the conditions in which the customer uses the product, or in the conditions in which the product is stored, or in how the product is maintained and serviced. 

Sjostrom, M. and Eriksson, L. Application of Statistical Experimental Design and PLS Modelling in QSAR. In QSAR Chemometric Methods in Molecular Design, Methods and Principles in Medicinal Chemistry, 2, Ed. H. van de Waterbeemd. Verlag Chemie, Weinheim, Germany, 1995... 

Fangmark I (1993), Formation of chlorinated aromatic compounds during incineration - an application of statistical experimental design", Dissertation, Universitat Ume3, Schweden Griffin RD (1987), Chemosphere 15 1987-1990. A new theory of dioxin formation in municipal solid waste combustion"... 

Lungmann, P., Choorit, W. Prasertsan, P. (2007). Application of statistical experimental methods to optimize medium for exopolymer production by newly isolated Halobacterium sp. SM5. Electron J Biotechnol, 10(1). 

Our discussion to this point has been confined to those areas in which the governing laws are well known. However, in many areas, information on the governing laws is lacking. Interest in the application of statistical methods to all types of problems has grown rapidly since World War II. Broadly speaking, statistical methods may be of use whenever conclusions are to be drawn or decisions made on the basis of experimental evidence. Since statistics could be defined as the technology of the scientific method, it is primarily concerned with the first two aspec ts of the method, namely, the performance of experiments and the drawing of conclusions from experiments. Traditionally the field is divided into two areas ... 

The relative error is the absolute error divided by the true value it is usually expressed in terms of percentage or in parts per thousand. The true or absolute value of a quantity cannot be established experimentally, so that the observed result must be compared with the most probable value. With pure substances the quantity will ultimately depend upon the relative atomic mass of the constituent elements. Determinations of the relative atomic mass have been made with the utmost care, and the accuracy obtained usually far exceeds that attained in ordinary quantitative analysis the analyst must accordingly accept their reliability. With natural or industrial products, we must accept provisionally the results obtained by analysts of repute using carefully tested methods. If several analysts determine the same constituent in the same sample by different methods, the most probable value, which is usually the average, can be deduced from their results. In both cases, the establishment of the most probable value involves the application of statistical methods and the concept of precision. 

Chapter 10, the last chapter in this volume, presents the principles and applications of statistical thermodynamics. This chapter, which relates the macroscopic thermodynamic variables to molecular properties, serves as a capstone to the discussion of thermodynamics presented in this volume. It is a most satisfying exercise to calculate the thermodynamic properties of relatively simple gaseous systems where the calculation is often more accurate than the experimental measurement. Useful results can also be obtained for simple atomic solids from the Debye theory. While computer calculations are rapidly approaching the level of sophistication necessary to perform computations of... 

Daniel, C. (1976), Applications of Statistics to Industrial Experimentation, Wiley, New York, NY. 

These two applications of statistics, from our point of view, will differ primarily in the kind of information we have available about our system. Sometimes, as when measuring micrographs, we have individual information on a large number of particles. Our question under these circumstances is how to condense these data into a few key parameters. In other circumstances, the experimental quantity itself will be an average quantity. Our question, then, is what kind of distribution is consistent with this average. In both cases, the underlying fact is the existence of a distribution of values for the quantity in question. We consider some aspects of these statistical topics here references in statistics should be consulted if additional information is needed. 

The single most important application of statistical methods in science is the determination and propagation of experimental uncertainties. Quantitative experimental results are never perfectly reproducible. Common sources of error include apparatus imperfections, judgments involved in laboratory technique, and innumerable small fluctuations in the environment. Does the slight breeze in the lab affect a balance When a motor starts in the next building, does the slight power surge affect a voltmeter Was the calibrated volumetric flask perfectly clean ... 

As drug development became of greater importance during the first half of the twentieth century, a more quantitative and analytical foundation was needed to assess drug potency per se as well as comparative drug potency. The standardization and quantification of technique and experimental design, and the rigorous application of statistical analysis, have provided pharmacodynamics with a necessary solid base. 

One of the most important areas of opportunity for the new application of statistical methods in the chemical industry in the twenty-first century is that of increasing the effectiveness of industrial experimentation. That is, it is one thing to bring an existing industrial process to stability (a state of... 

Before investigating these methods briefly, it will be necessary to become familiar with the terminology which is used in this particular application of statistical analysis. (The terminology is not always very meaningful in industrial problems since the early work in this area was originally developed in agricultural experimentation.)... 

Daniel C (1959) Technometrics 1 311 (b) Daniel C (1976) Application of statistics to industrial experimentation. Wiley, New York... 

In equation (49), which is the van t Hoff equation, —dH/de may be replaced by — AH, since these two quantities are equal for ideal-gas reactions. Relationships analogous to equation (49) may be derived for each of the equilibrium constants defined in Section A. 3, but for reactions in systems other than ideal-gas mixtures, — AH and — dH/de may not, in general, be equated in these expressions. Heats of reaction can be determined directly either by spectroscopic measurements followed by the application of statistical mechanics (for ideal-gas reactions) or by calorimetric measurements of Q (for arbitrary reactions). Since the measurement of equilibrium compositions may be simpler than either of the above procedures, in practice equation (49) is often used to obtain heats of reaction from experimental values of Kp at neighboring temperatures. 

Our major objective of this text is to provide a thorough background in those chemical principles that are particularly important to analytical chemistry. Second, we want students to develop an appreciation for the difficult task of judging the accuracy and precision of experimental data and to show how these judgments can be sharpened by the application of statistical methods. Our third aim is to introduce a wide range of techniques that are useful in modern analytical chemistry. Additionally, our hope is that with the help of this book, students will develop the skills necessary to solve analytical problems in a quantitative manner, particularly with the aid of the spreadsheet tools that are so commonly available. Finally, we aim to teach those laboratory skills that will give students confidence in their ability to obtain high-quality analytical data. 

Application of Statistics to Industrial Experimentation Wiley, New York 1976. 

In this brief survey many of the experimental and interpretive aspects of structural crystallography have been covered very lightly or not at all. For further details, the reader is referred to standard texts such as the one by Stout and Jensen.27 A useful guide to the applications of statistics to the interpretation of physical measurements, with particular emphasis on structural crystallography, is provided by Hamilton s excellent book.28 A useful survey of structural crystallography, which parallels this one in some aspects but provides more examples of the interpretation of structural results for organic molecules, has been given by Stewart and Hall.29... 

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