Statistical methods industrial experimentation

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. 

As described in several chapters of the present book [1,7], the application of pharmacokinetic (PK) and pharmacodynamic (PD) methods is widely accepted in the pharmaceutical industry. A PK model typically predicts the availability of a drug in the blood and interstitial spaces at different times after the drug has been administered. The model is used to determine characteristic parameters of the absorption, distribution, metabolism, and excretion processes from experimentally observed time courses, or the model follows the rates of formation and removal of various metabolites. PD models describe the effects of the drug (and its metabolites) as a function of time, again based on statistical fits to experimental results. 

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... 

It was evident that to apply tests of significance conveniently and economically the experiments had to be planned in appropriate forms. It is considered that the methods outlined should be as much a standard tool of the industrial experimenter as a chemical balance is of the laboratory experimenter. In carrying out an industrial experiment the choice is not between using a statistical design with the application of the appropriate tests of significance or the ordinary methods the choice is between correct or incorrect methods. Even the simplest experiment requires an estimate of the significance of its results. 

It was suggested that computer-based data analysis techniques (often involving multivariate statistical methods) can aid in this classification or simplification, as has been so profitable in other thermochemical conversion endeavours, for example, as applied to coal and petroleum. Again, it was emphasized that there is a need for a critical synthesis of the wealth of experimental data into regimes of behaviour, and simpler predictive equations or simulations, that are useful to the technologists in industry who are designing industrial scale reactors. 

From this point onwards, the paths diverge. One pathway, as used in this book so far, is to pursue the scientific study of the cytological, biochemical, and distributive clues that provided the lead in the first place. The other pathway is the statistical correlation of several physical properties of the lead molecule with its biological actions. It must be emphasized that statistics lies remote from experimental science and can, at best, indicate only a probability. However, these statistical methods are much used, particularly in industry, and it is proposed to give a brief account of correlation analysis (quantitative structure-activity relationships, or QSAR) which embodies them. 

By application of methods of experimental design, optimum conditions have been found for the preparation of a secondary amine [33]. We particularly recommend the paper of Meiners et al. [33] to the reader, inasmuch as it is one of the few reports describing a statistical design of experiments to a problem in organic synthesis, a procedure which is now finding more extensive application in the laboratory as well as in industry. 

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. 

Only applied originally in the pharmaceutical industry, automated synthetic methods have spread quickly into the research for new agrochemicals, other speciality chemicals, catalysts and new materials. It is also being used increasingly in process development laboratories coupled with statistical experimental design. 

A second example is provided by a semiempirical correlation for multi-component activity coefficients in aqueous electrolyte solutions shown in Fig. 2. This correlation, developed by Fritz Meissner at MIT [3], presents a method for scale-up activity-coefficient data for single-salt solutions, which are plentiful, are used to predict activity coefficients for multisalt solutions for which experimental data are rare. The scale-up is guided by an extended Debye-Hilckel theory, but essentially it is based on enlightened empiricism. Meissner s method provides useful estimates of thermodynamic properties needed for process design of multieffect evaporators to produce salts from multicomponent brines. It will be many years before sophisticated statistical mechanical techniques can perform a similar scale-up calculation. Until then, correlations such as Meissner s will be required in a conventional industry that produces vast amounts of inexpensive commodity chemicals. 

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.)... 

This design will not be discussed in detail as the author has not found instances in industrial work where the comparison of such large numbers of treatments is necessary. It is described here, however, as it is the simplest of a series of such designs. A general description with references is by F. Yates Empire Journal of Experimental Apiculture VIII, page 223, 1940. Descriptions and methods of computation of several are in C. H. Goulden "Methods of Statistical (John Wiley) 1939. 

In 2003, I wrote a book, Applied Statistical Designs for the Researcher (Marcel Dekker, Inc.), in which I covered experimental designs commonly encountered in the pharmaceutical, applied microbiological, and healthcare-product-formulation industries. It included two sample evaluations, analysis of variance, factorial, nested, chi-square, exploratory data analysis, nonpara-metric statistics, and a chapter on linear regression. Many researchers need more than simple linear regression methods to meet their research needs. It is for those researchers that this regression analysis book is written. 

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