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The extensive use of mathematical statistics for analyzing technological processes and constructing mathematical models is associated with the problem of creating automatic control systems and the development of engineering cybernetics. Statistical analysis of concentration processes has long been used, especially in calculations for assessing the process. However, it is only recently that mathematical statistics has been used to obtain quantitative characteristics and quantitative estimates of particular factors. In studying the flotation process we can use either traditional methods of statistical analysis such as dispersion, correlation, and regression analysis, or the new methods which have been developed in recent years.The primary problem in the flotation field is to create a unified system of investigation and analysis of the process, based on statistical methods. As we accumulate experience in the design of experiments for studying the concentratabiIities of ores, we may perhaps be able to standardize the methods of investigation.No less important are the laws of the industrial processes taking place in flotation plants. The engineering indices are subject to marked fluctuations owing to a number of factors, such as the quality of the original ore, the fineness to which it is crushed, the productivity, the expenditure of reagents, and so forth. Since these factors all vary simultaneously, we cannot separate and follow the effect of any one of them on the process or estimate the optimum values of the controllable parameters.These problems raise the question of working out the principles of design and automatic control of a concentration plant by statistical methods and models. We must emphasize that the use of statistical methods is based on a number of important postulates. These postulates create some difficulties, both of a general nature and of a type specific to the concentration of minerals.Among the commonest errors we may cite neglect of the distribution of the parameters, which must be nearly normal (or reducible to normal) if we are to use dispersion, correlation, and regression analysis [1]. The difficulty of assessing normality or of replacing the parameters by functions (e.g., by the logarithmic function in the case of a log-normal distribution) forces us to make use of the hypothesis of a priori normality. In fact, however, for an output parameter which is expressed by "normalized" quantities in engineering processes, the normal distribution is the exception rather than the rule. Such quantities include the metal content of the concentration products, the extraction rate, the yield, the deviation from the set conditions, and so on. Normalized parameters (expressed as a percentage or fraction) vary over some range. This range is often narrower than 0-100%: for instance, the metal content of a concentrate is limited by the theoretically possible content in the mineral, while the yield and extraction are limited by the process conditions. Since the normal distribution runs from -~o to + co appro...
The extensive use of mathematical statistics for analyzing technological processes and constructing mathematical models is associated with the problem of creating automatic control systems and the development of engineering cybernetics. Statistical analysis of concentration processes has long been used, especially in calculations for assessing the process. However, it is only recently that mathematical statistics has been used to obtain quantitative characteristics and quantitative estimates of particular factors. In studying the flotation process we can use either traditional methods of statistical analysis such as dispersion, correlation, and regression analysis, or the new methods which have been developed in recent years.The primary problem in the flotation field is to create a unified system of investigation and analysis of the process, based on statistical methods. As we accumulate experience in the design of experiments for studying the concentratabiIities of ores, we may perhaps be able to standardize the methods of investigation.No less important are the laws of the industrial processes taking place in flotation plants. The engineering indices are subject to marked fluctuations owing to a number of factors, such as the quality of the original ore, the fineness to which it is crushed, the productivity, the expenditure of reagents, and so forth. Since these factors all vary simultaneously, we cannot separate and follow the effect of any one of them on the process or estimate the optimum values of the controllable parameters.These problems raise the question of working out the principles of design and automatic control of a concentration plant by statistical methods and models. We must emphasize that the use of statistical methods is based on a number of important postulates. These postulates create some difficulties, both of a general nature and of a type specific to the concentration of minerals.Among the commonest errors we may cite neglect of the distribution of the parameters, which must be nearly normal (or reducible to normal) if we are to use dispersion, correlation, and regression analysis [1]. The difficulty of assessing normality or of replacing the parameters by functions (e.g., by the logarithmic function in the case of a log-normal distribution) forces us to make use of the hypothesis of a priori normality. In fact, however, for an output parameter which is expressed by "normalized" quantities in engineering processes, the normal distribution is the exception rather than the rule. Such quantities include the metal content of the concentration products, the extraction rate, the yield, the deviation from the set conditions, and so on. Normalized parameters (expressed as a percentage or fraction) vary over some range. This range is often narrower than 0-100%: for instance, the metal content of a concentrate is limited by the theoretically possible content in the mineral, while the yield and extraction are limited by the process conditions. Since the normal distribution runs from -~o to + co appro...
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