Article 14419

Title of the article

IMPROVING THE EFFICIENCY OF THE HOTELLING ALGORITHM WHEN EVALUATING THE STABILITY OF AN OBJECT 

Authors

Klyachkin Vladimir Nikolaevich, doctor of technical sciences, professor, sub-department of applied mathematics and informatics, Ulyanovsk State Technical University (432027, 32 Severny Venec street, Ulyanovsk, Russia), E-mail: v_kl@mail.ru
Karpunina Irina Nikolaevna, candidate of technical sciences, associate professor, sub-department of general professional disciplines, Ulyanovsk Institute of Civil Aviation (432071, 8/8 Mozhaiskiy street, Ulyanovsk, Russia), E-mail: karpunina53l@yandex.ru
Kravtsov Yuriy Andreevich, candidate of technical sciences, associate professor, sub-department of applied mathematics and informatics, Ulyanovsk State Technical University (432027, 32 Severny Venec street, Ulyanovsk, Russia), E-mail: ukravtsov@rambler.ru
Bubir Dmitry Sergeevich, candidate of technical sciences, senior researcher, Ulyanovsk Design Bureau of Instrumentation (432017, 10 Krymova street, Ulyanovsk, Russia), E-mail: bubir91@mail.ru 

Index UDK

681.518.5 

DOI

10.21685/2307-4205-2019-4-14 

Abstract

Background. The functioning of a complex system depends on the totality of many indicators. To assess the stability of the operation of an object, methods of multivariate statistical control are used, which allow the prediction of a violation by the nature of the change in the statistical characteristics of the process before the stability of the operation of the object is violated. If there are correlated indicators of the object's operation, the stability of its functioning can be controlled using the Hotelling algorithm. To increase the sensitivity of this algorithm to possible process violations, two approaches are proposed. The first proposes a search on the Hotelling chart for nonrandom structures whose probability of occurrence is commensurate with the probability of false alarm: the presence of such a structure on the map indicates a violation of stability. The second approach uses a warning boundary on the chart: hitting several points in a row between the control and warning boundaries also indicates the instability of the process. Both approaches involve the use of special software to automate the search for violations.
Materials and methods. When determining the parameters of nonrandom structures in multivariate control, probabilistic methods are used. The position of the warning and control boundaries is calculated using Markov chains; the results are approximated by regression analysis methods. The effectiveness of the proposed approaches is estimated by the average run length – the number of observations from the moment of violation of the process of functioning of the object to the moment of detection of this violation.
Results. The application of the proposed approaches to increase the sensitivity of the Hotelling algorithm to possible process disturbances ensures the fastest detection of the instability of the object's functioning. 

Key words

stability of the functioning, control chart, nonrandom structures, warning limit, the average run length 

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Дата создания: 03.02.2020 16:34
Дата обновления: 04.02.2020 11:18