On the Comparative Efficiency of Change Point Detection in Multivariate Technological Processes Using Multidimensional Double Control Charts

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Resumo

The problem of change point detection in multiparametric technological processes having a normal distribution and consisting in a shift from a given value of the sample mean and sample variance is investigated. Various types of control charts are considered, which make it possible to effectively detect simultaneous changes in the mean value and variance in multiparametric technological processes. By the method of statistical modeling, an analysis of the comparative effectiveness of control charts is carried out, practical recommendations are given.

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Sobre autores

Alexander Chesalin

MIREA – Russian Technological University

Email: chesalin_an@mirea.ru
ORCID ID: 0000-0002-1154-6151

Candidate of Engineering; Head of the Department of Computer and Information Security of the MIREA – Russian Technological University

Rússia, Moscow

Sergey Grodzensky

MIREA – Russian Technological University

Email: chesalin_an@mirea.ru
ORCID ID: 0000-0003-1965-5624

Doctor of Engineering, Professor; Professor at the Department of Computer and Information Security of the MIREA – Russian Technological University

Rússia, Moscow

Nadezhda Ushkova

MIREA – Russian Technological University

Email: chesalin_an@mirea.ru

assistant at the Department of Computer and Information Security of the MIREA – Russian Technological University

Rússia, Moscow

Kirill Bolotin

MIREA – Russian Technological University

Email: chesalin_an@mirea.ru

assistant at the Department of Computer and Information Security of the MIREA – Russian Technological University

Rússia, Moscow

Alexey Stavtsev

MIREA – Russian Technological University

Autor responsável pela correspondência
Email: chesalin_an@mirea.ru

Candidate of Physics and Mathematics; associate professor at the Department of Computer and Information Security of the MIREA – Russian Technological University

Rússia, Moscow

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2. Fig. 1. Stable state of the process (gray dots) and three cases of breakdown (red dots): a – by shifting the average value; b – by increasing the spread; c – by simultaneously shifting the average value and increasing the spread

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3. Fig. 2. Block diagram of the simulation algorithm

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4. Table 1. ASN heat maps of the studied control charts for the case of the average correlation ρij ∈ [0,4; 0,6], five controlled parameters and simultaneous changes in µ and σ for all controlled parameters

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5. Table 2. Heat maps of the evaluation of the relative efficiency of the studied control charts with a different number of controlled parameters (2, 5, 10 parameters) for the case of the average correlation ρij ∈ [0,4; 0,6], simultaneous changes in µ and σ of all controlled parameters

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6. Table 3. Heat maps of the evaluation of the relative effectiveness of the studied control charts with a change in the correlation value (strong correlation – ρij ∈ [0,1; 0,3], medium – ρij ∈ [0,4; 0,6], high – ρij ∈ [0,7; 0,9]) for the case of five controlled parameters and their simultaneous change

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7. Table 4. Heat maps of the evaluation of the relative effectiveness of the studied control charts when changing the number of parameters to be changed (1, 3, 5 parameters) for the case of the average correlation ρij ∈ [0,4; 0,6] and five controlled parameters

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