
Main / Anastasiia Valerevna Alekseeva
Author: "Anastasiia Valerevna Alekseeva"
Vladimir Nikolaevich Kliachkin, Doctor of Sciences in Engineering; Professor; graduated from the Mechanical Faculty of Ulyanovsk Polytechnic Institute; Professor at the Department of Applied Mathematics and Informatics of Ulyanovsk State Technical; an author of scientific works in the field of reliability and statistical methods. email: v_kl@mail.ruV.N. Kliachkin,
Anastasiia Valerevna Alekseeva, graduated from the Faculty of Information System and Technologies of Ulyanovsk State Technical University; Postgraduate Student at the Department of Applied Mathematics and Informatics of UlSTU, Standardization Engineer at the Ulyanovsk Design Bureau of Instrumentation; an author of articles in the field of the statistical methods in quality control. email: age89@mail.ruA.V. Alekseeva 

Optimization of parameters of generalized dispersion algorithm at statistical process control
When monitoring a real production process using statistical methods, the question of early detection of violations arises. In most cases, several indicators are monitored simultaneously in the production process, and a change in the values of some indicators leads to a change in others. If there is a dependence of indicators for their monitoring, multivariate statistical control tools are used, in particular generalized variance chart. By varying the parameters of the chart, its efficiency can be significantly increased, this allows minimizing the time the process is in an unstable state. Applying the approach of A. Duncan, which he developed for Shewhart charts, a formula for the expectation of the duration of an unstable state of a process was obtained and a Python program was developed to minimize it. To test the set optimization problem, the calculation of the data of two process indicators is given and the optimal parameters of the generalized variance chart are obtained, at which the duration of the process in an unstable state is minimal.
Scattering stability, generalized variance, duration of unstable process state, optimization task.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Anastasiia Valerevna Alekseeva, Postgraduate Student of the Department of Applied Mathematics and Informatics of Ulyanovsk State Technical University; graduated from the Faculty of Information Systems and Technologies at UlSTU; a standardization engineer at the Ulyanovsk Instrument Manufacturing Design Bureau, JSC; an author of scientific publications in the field of the statistical methods in quality management. email: age 89@mail.ruA.V. Alekseeva


Improving the efficiency of statistical control of hydrounit vibrations
Some techniques of statistical process control can be applied in investigating an object for likely defects. In this regard, the multidimensional scattering is monitored with the use of a generalized variance algorithm. At fixed time intervals samples of observations are recorded, according to which the values of the determinant of covariance matrix (the generalized variance) are calculated. The corresponding point, falling outside the borders of control chart, indicates the process failure. The test results based on vibration data obtained from the hydraulic unit at the Krasnopolianskaia Hydroelectric Power Station showed that the algorithm of the generalized variance has an insufficient quick response relating to both gradual and spasmodic changes in the scattering level. To make the monitoring process more efficient, the following techniques have been suggested. The first one detects defects by analyzing special kind structures on the generalized variance chart. The second technique applies the warning borders on the chart and the third one implies an algorithm of exponentially weighted moving averages for generalized variance. All the tests revealed that the search for nonrandom structures on the generalized variance chart is most effective for the early detection of changes in the scattering process
Generalized variance, average run length, hydraulic unit vibrations, warning borders, exponentially weighted moving averages.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
Vladimir Nikolaevich Kliachkin, Doctor of Sciences in Engineering, Professor; graduated from the Faculty of Mechanics of Ulyanovsk Polytechnic Institute; Professor at the Department of Applied Mathematics and Informatics of Ulyanovsk State Technical University; an author of scientific publications in the field of reliability, statistical methods. email: v_kl@mail.ruV.N. Kliachkin
Anastasiia Valerevna Alekseeva, Postgraduate Studentatthe Departmentof Applied Mathematics and Informatics of UlSTU; graduated from the Faculty of Information System and Technologies of UlSTU; a standardization engineer at the Ulyanovsk Design Bureau of Instrumentation, JSC; an author of scientific publications in the field of statistical methods of quality control. email: age89@mail.ruA.V. Alekseeva


Study of the efficiency of statistical control of hydrounit vibrations
To diagnose the technical condition of the hydraulic unit, vibration monitoring is carried out, as the level of vibration largely determines the quality of operation of the unit. When assessing the stability of vibrations, methods of statistical process control can be used. Many monitored indicators include both independent and correlated indicators. When monitoring correlated indicators, multivariate control methods are used. Midlevel monitoring of the process is based on the Hotelling algorithm. For the analysis of multivariate scattering, the generalized dispersion algorithm is used. The methodology and test results for analyzing the effectiveness of the generalized dispersion algorithm for controlling multidimensional vibration scattering are considered. Regression dependences of the average run length on the characteristics of the process disturbance were constructed, on the basis of which the quality of vibration diagnostics can be estimated. Initially, a lot of samples are constructed that are identical to the studied process of vibration of the hydraulic unit, that is, with a vector of average and covariance matrix corresponding to the training sample obtained in the real process. Based on the results of statistical tests, regression dependences of the average length of the series on the characteristics of the process violation were obtained, on the basis of which the quality of vibration diagnostics can be estimated.
Vibration stability, multivariate scattering, generalized dispersion, average run length.



Sections: Mathematical modeling
Subjects: Mathematical modeling. 
