Statistical methods design experiments

Fisher was a pioneer in developing and using statistics to design and interpret experiments. He coined the term variance (Fisher, 1918) and wrote what became the standard reference entitled Statistical Methods for Research Workers. He advocated the use of statistics to design experiments systematically. 

Densification processes involve large populations of randomized particles in randomized local environments, and are thus statistical in character hence statistical methods of experiment design and analysis, together with computer processing of data, are likely to be appropriate and desirable. 

Cropley made general recommendations to develop kinetic models for compUcated rate expressions. His approach includes first formulating a hyperbolic non-linear model in dimensionless form by linear statistical methods. This way, essential terms are identified and others are rejected, to reduce the number of unknown parameters. Only toward the end when model is reduced to the essential parts is non-linear estimation of parameters involved. His ten steps are summarized below. Their basis is a set of rate data measured in a recycle reactor using a sixteen experiment fractional factorial experimental design at two levels in five variables, with additional three repeated centerpoints. To these are added two outlier... 

A problem may lie in the knowledge that is required as an essential input to such approaches, being both statistical in nature and from the authors own experiences, often diificult to obtain and interpret generally. Unfortunately, experienced designers will not use statistical methodology, although statistical methods should play an important role in the design and manufacture of reliable products (Amster and... 

Statistical benefit Using statistical methods in the design of experiments and data analy-... 

Gart, J. J., Krewski, D., Lee, P. N., Tarone, R. E. and Wahrendorf, J. (1986). The design and analysis of long-term animal experiment, in Statistical Methods in Cancer Research, Vol. III. IARC Scientific Publication No. 79. International Agency for Research on Cancer Lyon. 

Chemometrics is the chemical discipline that uses mathematical and statistical methods select optimal measurement procedures and experiments, and (b) to provide maximum chemical information by analyzing chemical data."(I)... 

The PAT guidance facilitates introduction of new measurement and control tools in conjunction with well-established statistical methods such as design of experiments and statistical process control. It, therefore, can provide more effective means for product and process design and control, alternate efficient approaches for quality assurance, and a means for moving away from the corrective action to a continuous improvement paradigm. 

V.V. Nalimov and N.A. Chernova, Statistical methods of design of extremal experiments, Nauka, Moscow, 1965 (in Russian)... 

Furthermore, it has been clearly pointed out [127] that, once a large number of experiments of more or less arbitrary design have been performed, a posterior use of statistical methods of data treatment can no longer guarantee a result of reliable value, because... 

Statistically designed experiments were carried out to assess the reproducibility of the method as applied to both solid isolates and broth samples. 

However, it should be emphasized that the statistical methods presented here are no cures for poor data. Irrelevant or erroneous measurement and poorly planned experiments will still be irrelevant, erroneous and poorly planned in spite of any statistical analysis. There are, however, many examples of excellent data that have been seriously mutilated by poor statistical analysis. The aim of this chapter is to present multivariate statistical methods for design and... 

Finally, it should be pointed out once again that obtaining as precise and complete information on a studied chemical or physical system as possible, with a minimal number of experiments and the lowest possible expenses, is the necessary condition for efficient research work. Therefore, application of modern mathematical and statistical methods in designing and analyzing experimental results is a real necessity in all fields and phases of work, starting with purely theoretical considerations of a process, its research and development, all the way to designing equipment and studying optimal operational conditions of a plant. 

Factorial design of experiments, combined with statistical methods of data analysis, offers wider and more differentiated information on the system, while conclusions are of greater usability. The results of all the eight runs in the analyzed example serve for determining the factor effects, with seven trials being independent possibilities of testing the effects and one serving for their comparison with the chosen fixed values. Three out of seven independently determined factor effects serve for... 

The last twenty years of the last millennium are characterized by complex automatization of industrial plants. Complex automatization of industrial plants means a switch to factories, automatons, robots and self adaptive optimization systems. The mentioned processes can be intensified by introducing mathematical methods into all physical and chemical processes. By being acquainted with the mathematical model of a process it is possible to control it, maintain it at an optimal level, provide maximal yield of the product, and obtain the product at a minimal cost. Statistical methods in mathematical modeling of a process should not be opposed to traditional theoretical methods of complete theoretical studies of a phenomenon. The higher the theoretical level of knowledge the more efficient is the application of statistical methods like design of experiment (DOE). 

To design an experiment means to choose the optimal experiment design to be used simultaneously for varying all the analyzed factors. By designing an experiment one gets more precise data and more complete information on a studied phenomenon with a minimal number of experiments and the lowest possible material costs. The development of statistical methods for data analysis, combined with development of computers, has revolutionized the research and development work in all domains of human activities. 

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