### Journals Information

Mathematics and Statistics Vol. 10(3), pp. 463 - 467
DOI: 10.13189/ms.2022.100301
Reprint (PDF) (335Kb)

## Three-Dimensional Control Charts for Regulating Processes Described by a Two-Dimensional Normal Distribution

Kamola Saxibovna Ablazova *
Faculty of Mathematics and Physics, Andijan State University, Republic of Uzbekistan

ABSTRACT

In the statistical management of processes in the initial phase, the stability of the technological process is determined based on the available samples. If the process is not stable, eliminating possible causes is brought into a statistically controlled position. At the same time, simple Shewhart control charts are used. In practice, some methods bring the process to a stable state (ISO standards, standards of various states). After the process has become stable, the boundaries of control charts are found for further management. Then, with the help of new samples, the process is managed. The article considers a process modeled by a two-dimensional normal distribution. New control charts have been found to check the normality and correlation of two-dimensional random variable components. The process is regulated using these charts, preserving the shape of the density of the individual components of the normal vector and linearity of these components. When constructing control charts, the Kolmogorov-Smirnov type agreement criterion and the Fisher criterion on the strength of the linear coupling of components were used. A concrete example shows the course of the introduction of these charts in production. The work results can be used in the initial phase of regulation and during the control check of the process under study. We used these control charts to assess product quality and quality control coming from the machine that produces the sleeves. It presents statistical methods for analyzing problems in factory practice and solutions for their elimination.

KEYWORDS
Statistical Control of Production, Control Charts, Statistical Hypothesis, Kolmogorov-Smirnov Type Consent Criterion, Fisher Criterion, Machine Operation Control

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Kamola Saxibovna Ablazova , "Three-Dimensional Control Charts for Regulating Processes Described by a Two-Dimensional Normal Distribution," Mathematics and Statistics, Vol. 10, No. 3, pp. 463 - 467, 2022. DOI: 10.13189/ms.2022.100301.

(b). APA Format:
Kamola Saxibovna Ablazova (2022). Three-Dimensional Control Charts for Regulating Processes Described by a Two-Dimensional Normal Distribution. Mathematics and Statistics, 10(3), 463 - 467. DOI: 10.13189/ms.2022.100301.