A study of statistical and deterministic models for the prediction of the composition of a mixture

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Virginia Tech

This thesis is a study of various physical and statistical models which may be useful for the prediction of the composition of a ternary liquid mixture. The particular mixture considered in this study was the solvent system consisting of nitroglycerine (NG), 2-nitrodiphenylamine (2NDPA), and triacetin (TA). Several models were investigated for their adequacy and closeness of fit. An attempt has been made to relate the actual composition to a few easily measurable quantities, namely, refractive index, density, and the separate analysis of 2NDPA.

Deterministic models relating the concentration of each component in the mixture with the physical determinations mentioned above have been considered first. These models are based on the known theory of physical chemistry. The deterministic model which was chosen as "best" in terms of the smallness of error of prediction, estimates the composition from the determination of density and the spectrophotometer analysis of 2NDPA. Since the latter analysis is a quick and accurate determination of the 2NDPA content and since the content of the third component could be determined by complementing to 100 percent, the models have been formulated in terms of the concentration of only one component, namely NG.

The statistical models under investigation are divided into activity models and regression models. The activity model is a combination of chemical and statistical theory while the simple regression model represents an approach that a statistician might take if he disregarded the physical or chemical theory involved. Two activity models have been discussed, the first assuming the activity of the mixture constant and the second assuming the activity of the mixture to be a weighted sum of the activities of the three components.

Tests of hypotheses are made to determine whether the activity models result in a significant reduction in error over that of the "best" deterministic model. The investigation that the model formulated assuming constant activity of the mixture results in the smallest error of estimation among all models under study. Thus it has been used as a basis for the preparation of control charts.

The linear regression models, constructed with various functions of density, refractive index, and spectrophotometer analysis as independent variables, produced errors of estimation above those for the deterministic model.

Chapter IV represents the summary of the thesis and the translation of findings into actual control charts. On the basis of this chapter, a technician can easily determine the estimate of the composition of the mixture and the attached 99 percent confidence bounds. Thus, this Chapter contains these charts combined with instructions in their use and numerical examples.