Scientific Journal of KubSAU

The article analyzes the development of the theory of statistical control (from the XVIII century to the present). Prof. M.V. Ostrogradskii (1846) clearly describes the practical needs (ie, arising from the quality assurance of large quantities of bags of flour or pieces of cloth), to meet whom he spent his research. At the same time Simpson was among the ideas of probability theory XVIII century. Therefore prof. M.V. Ostrogradskii may be regarded as the founder of the theory of statistical process control (not only in our country but all over the world). Limit theorems of probability theory and mathematical statistics have provided a number of asymptotic results in problems of statistical quality control, offer based on these best practices. However, we must find out how much interest among specialists characteristics are different from limit for finite sample sizes. Such research for the synthesis algorithm control plan on the basis of the limit average output level of defects is made in this article, and for the synthesis algorithm control plan on the basis of the acceptance and the rejection levels of defects - not yet (clarification of the conditions of applicability of this algorithm - unsolved problem of applied mathematics). We have briefly reviewed the development of our researches on the statistical control. Control units can be not only some units of production, but also documents (with internal and external audit), and standard units of air, water and soil in the environmental monitoring. One of the achievements can be regarded as the transfer of statistical control of production for environmental monitoring

Controlling of statistical methods to ensure product quality is the special case of controlling organizational and economic methods of management. Today, controlling in the practice of management of Russian companies is understood as "the system of information-analytical and methodological support to achieve their goals." The controller is developing a decision-making rules, the head takes decisions on the basis of these rules. We proved the concept of "controlling of methods". Innovation in management is based, in particular, on the use of new adequate organizational-economic (as well as economicmathematical and statistical) methods. Controlling in this area - is the development and application procedures of compliance management used and newly developed (implemented) organizationaleconomic methods for the task. Thus, the methodology for controlling is of great practical value in any field in which the actions (operations) must be carried out in accordance with certain rules (regulations, standards, guidelines), as in any such area in which we need to use development and application procedures of compliance management used and the newly established (implemented) rules for solution of tasks assigned to the organization. In this article, we select a area of controlling as controlling quality, and we discuss its main issues. This is about controlling of organizational-economic methods to ensure product quality, especially about the statistical methods based on probability theory and mathematical statistics. We consider the analysis and synthesis of plans of statistical quality control, optimization options plans of statistical control, truncated plans. Are discussed the differences control plans provider and the consumer, the allocation of units formless (liquid, gas) products, the selection of a random sample of the statistical quality control of products, lower estimate of the required sample size. It is established, that is not always necessary quality control. Is given the theory of the basic paradox of statistical quality control. We discuss the development of statistical methods for quality control in our country. Is given the classification of statistical methods of quality management

Of the many urgent problems of Science about Science, we consider methods for estimation of the effectiveness and quality of the scientific activities of the researcher, of the organization, of the magazine. Performance indicators of scientific activity are used as an important part in the estimation of higher education institutions, the innovative capacity of enterprises, etc. To estimate the effectiveness of scientific activity is natural to use intellectual tools which are well-established in other subject areas. This will include, in particular, the balanced scorecard, based on key performance indicators (hence the title of this article), as well as controlling, primarily controlling of research activities. There are two more developed and widely used tools for estimation the effectiveness of the scientific activity - the scientometric indicators and the expert estimators. Their critical analysis is the subject of this article. Different versions of manipulating of values of scientometric indicators in the Russian Federation, in our estimation, are still relatively rare. Perhaps this is due to the relatively short period of their use in the management of science. Since an indicator such as citation index (the number of citations of publications) of researcher, allows estimating its contribution to science, the use of this scientometric indicator for the management of science is justified. At the same time, the number of publications and especially h-index is not possible to objectively estimate the effectiveness of research activities, particularly in view of the properties of the real bibliometric databases. Expert procedures have several disadvantages. In this article we discuss the real effectiveness of expert procedures in the areas of their application, as conferring academic degrees and elections to the National Academy of Sciences (primarily in the Russian Academy of Sciences). The basic principles of expertise in these areas remain the same for the past 70 years. Based on an analysis of practice it is necessary to ascertain the lack of efficacy of expert estimators in these areas. Rationale to what has been said is given in the article

Sociology is one of the most important social sciences. Mathematical and primarily statistical methods are effective intellectual tools of sociologists. Let us analyze the work of the author of this article on the development of statistical methods to meet the challenges of sociology. Then we give the review of development of statistical methods in Russian sociology for 45 years (1970-2015). The basic scientific events of these years, first of all, were formation of applied statistics and its basis - statistics of the non-numerical data (in sociology of 70-90% of variables have non-numerical nature). Over the last 30 years, the Russian sociology has been growing rapidly in all quantitative parameters. Clearly, the depth of investigation gives the use of advanced scientific apparatus - methodology and methods of data collection and analysis, mathematical models. In our view, a fundamental breakthrough was made in our country in the 1970s. It was then in the arsenal of Russian sociologists appeared measurement theory and fuzzy sets, mathematical methods of classification and multidimensional scaling, nonparametric statistics and statistics of non-numeric data. In subsequent decades it has been a natural development of scientific apparatus. The same mathematical and statistical methods and models can be successfully applied in various fields of science and practice. Statistical methods and models are very effective in sociological, socio-economic, managerial, technical and feasibility studies, medicine, history, in almost any industry and application areas of knowledge. Within this field, the main event of the last thirty five years - is becoming a scientific and practical discipline "Applied Statistics", dedicated to the development and application of statistical methods and models. An analysis of the dynamics of applied statistics leads to the conclusion that in the XXI century the statistics of non-numerical data is becoming a central area of applied statistics, as it contains the most common approaches and results

Estimates of the errors of the characteristics of financial flows of investment projects are needed to make adequate management decisions, particularly in the rocket and the space industry. Organizational-economic approaches to the estimations of the feasibility of innovation-investment projects to create rocket and space technologies require intensive use of numerical characteristics of the financial flows of long-term projects of this type. In organizational-economic support for control problems in the aerospace industry we must provide the need to obtain the estimates of the errors of the characteristics of financial flows. Such estimates are an integral part of the organizational-economic support of innovation activity in the aerospace industry. They can be compared with the predictions interval, i.e. confidence estimation of predictive values. Half the length of the confidence interval is the prediction error estimate. In this article we give the new method for estimating the errors of the main characteristics of the investment projects. We focus on the net present value called NPV. Our method of estimation of errors is based on the results of statistics interval data, which is an integral part of the system fuzzy interval mathematics. We construct asymptotic theory which corresponds to small deviations of discount coefficients. The error of NPV has been found as the asymptotic notna. With up to infinitesimals of higher orders the error of NPV is a linear function of the maximum possible error of discount coefficients

According to the new paradigm of applied mathematical statistics one should prefer non-parametric methods and models. However, in applied statistics we currently use a variety of parametric models. The term "parametric" means that the probabilistic-statistical model is fully described by a finite-dimensional vector of fixed dimension, and this dimension does not depend on the size of the sample. In parametric statistics the estimation problem is to estimate the unknown value (for statistician) of parameter by means of the best (in some sense) method. In the statistical problems of standardization and quality control we use a three-parameter family of gamma distributions. In this article, it is considered as an example of the parametric distribution family. We compare the methods for estimating the parameters. The method of moments is universal. However, the estimates obtained with the help of method of moments have optimal properties only in rare cases. Maximum likelihood estimation (MLE) belongs to the class of the best asymptotically normal estimates. In most cases, analytical solutions do not exist; therefore, to find MLE it is necessary to apply numerical methods. However, the use of numerical methods creates numerous problems. Convergence of iterative algorithms requires justification. In a number of examples of the analysis of real data, the likelihood function has many local maxima, and because of that natural iterative procedures do not converge. We suggest the use of one-step estimates (OS-estimates). They have equally good asymptotic properties as the maximum likelihood estimators, under the same conditions of regularity that MLE. One-step estimates are written in the form of explicit formulas. In this article it is proved that the one-step estimates are the best asymptotically normal estimates (under natural conditions). We have found OS-estimates for the gamma distribution and given the results of calculations using data on operating time to limit state for incisors

Statistical methods are based on the developed theory and demonstrated its usefulness in the sectors of the economy. However, the analysis of the situation in the application of statistical methods shows obvious distress, in which accumulated in our country's scientific potential is not used to the full. As practice shows, it is not enough to develop promising modern theory-based effective mathematical and instrumental methods of controlling. For using such methods in mass, it is necessary that they would be implemented. Management of innovations, i.e. innovation management, quite rightly is currently one of the most debated sections of the economy and the organization of production, of the entire economic science in general. However, the implementation of applied statistics and other statistical methods, more generally, mathematical and instrumental methods of controlling, has its own specifics. It is considered in the article. We have highlighted the developmental vulnerabilities - low scientific level of many individuals applying statistical methods, the lack of organizational structure of applied statistics as a field of applied activities and others. We regret to note that the very idea of the need to establish requirements for the methods of data analysis and project formulations such requirements remained outside the attention of those professionals who need them and were addressed. We have no adequate system of guidance for documents on concrete statistical methods performed on modern scientific level. According to the author, the desired future of applied statistics is reorganization according to the model of Metrology. We have analyzed the application of statistical methods as a specialty. The analysis of state standards on statistical methods and the causes of them blunders are given. We have discussed the status of documents for statistical methods for standardization and quality control. We discuss a new system of "Six Sigma" for implementation advanced mathematical and instrumental methods of controlling

The mathematical theory of classification contains a large number of approaches, models, methods, algorithms. This theory is very diverse. We distinguish three basic results in it - the best method of diagnosis (discriminant analysis), an adequate indicator of the quality of discriminant analysis algorithm, the statement about stopping after a finite number of steps iterative algorithms of cluster analysis. Namely, on the basis of Neyman - Pearson Lemma we have shown that the optimal method of diagnosis exists and can be expressed through probability densities corresponding to the classes. If the densities are unknown, one should use non-parametric estimators of training samples. Often, we use the quality indicator of diagnostic algorithm as "the probability (or share) the correct classification (diagnosis)" - the more the figure is the better algorithm is. It is shown that widespread use of this indicator is unreasonable, and we have offered the other - "predictive power", obtained by the conversion in the model of linear discriminant analysis. A stop after a finite number of steps of iterative algorithms of cluster analysis method is demonstrated by the example of k-means. In our opinion, these results are fundamental to the theory of classification and every specialist should be familiar with them for developing and applying the theory of classification

Based on an objective analysis, it must be noted that in the arsenal of managers, especially foreign ones, there is practically no fundamentally new methods and tools. However, promising mathematical and instrumental methods of controlling actively developed in our country. In the XXI century it developed a new paradigm of mathematical methods of economics and produced more than 10 books, developed in accordance with this paradigm. The new paradigm is based on the modern development of mathematics as a whole - on the system interval fuzzy math. The new paradigm offers tools used non-parametric statistics, which suggest that the distribution functions are arbitrary. In 1979 it was allocated one of the four major areas of modern applied statistics - statistics of objects of nonnumeric nature (statistics of non-numeric data, nonnumeric statistics). The other three - statistics of random variables, multivariate statistical analysis, statistics of random processes and time series. Statistics of objects of non-numeric nature is central to the modern mathematical methods of economics. On the basis of modern information-communication technologies we have developed a new economic theory - solidary information economy. New intellectual tools of controlling include an automated system-cognitive analysis (ASA) and its software - the system of "Eidos". The systems approach to solving specific applications often requires going beyond the economy. Very important are the procedures for the introduction of innovative methods and tools

Econometrics is one of the most effective mathematical tools of controlling. The article deals with general problems of application of econometric methods in solving problems of controlling. Econometric methods - is primarily a statistical analysis of concrete economic data, of course, with the help of computers. In our country, they are still relatively little known, even though we have the most powerful scientific school in the foundations of econometrics - the probability theory. The article shows that to decide the problems of controlling is necessary to apply econometric methods. Classification of econometric tools can be carried out on various grounds: on methods, by type of data, in tasks, etc. Mass introduction of software products, including modern econometric analysis tools of concrete economic data can be regarded as one of the most effective ways to accelerate scientific and technological progress. The whole arsenal currently used econometric and statistical techniques (methods) can be divided into three streams: high econometric (statistical) technology; classical econometric (statistical) technology, low (inadequate, obsolete) econometric (statistical) technology. The main problem of modern econometrics is to ensure that the concrete econometric and statistical studies used only the first two types of technology. To get a broader representation of the use of econometric methods in the management of production organization we analyze basic textbook "Organization and planning of engineering production (production management)," prepared by the Department of "Economics and organization of production" of the Bauman Moscow State Technical University. It has more than 20 times using econometric methods and models that testify to the effectiveness of such a tool of manager as econometrics