ISSN 1991-2927
 

ACP № 1 (59) 2020

Author: "Ekaterina Aleksandrovna Zentsova"

Vladimir Nikolaevich Kliachkin, Ulyanovsk State Technical University, Doctor of Engineering; graduated from the Mechanical Faculty of Ulyanovsk Polytechnic Institute; Professor at the Department of Applied Mathematics and Informatics of Ulyanovsk State Technical University; an author of scientific works in the field of reliability and statistical methods. [e-mail: v_kl@mail.ru]V. Kliachkin,

Ekaterina Aleksandrovna Zentsova, Ulyanovsk State Technical University, graduated from the Faculty of Information Systems and Technologies of Ulyanovsk State Technical University; Postgraduate Student at the Department of Applied Mathematics and Informatics of Ulyanovsk State Technical University; an author of scientific papers in the field of statistical process control. [e-mail: e_zentsova@mail.ru]E. Zentsova

Design of an Adaptive Control Scheme for Multivariate Statistical Process Control 000_6.pdf

Statistical control of a technological process is used in order to guarantee the required quality level by implementing timely corrective actions when the process is instable. Quality of a product manufactured in a technological process is usually measured by multiple quality characteristics, part of them are correlated. Statistical control is carried out separately for groups of correlated and independent characteristics. Independent quality characteristics of a technological process can be controlled with standard Shewhart’s control charts. In order to monitor a set of correlated characteristics, a multivariate Hotelling’s control chart is used. The main purpose of this chart is to observe multivariate process settings level. This chart quickly detects large shifts in the multivariate process mean and often ignores small ones. In order to improve its performances in detecting small shifts in the mean vector, the adaptive control scheme design is proposed. Its parameters change according to predictions based on the current process status observations. The characteristics of different adaptive control schemes are designed in a standardized fashion to ensure the comparison of these schemes is meaningful and unbiased.

Adaptive control scheme, hotelling’s control chart, markov chains.

2017_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.


Ekaterina Aleksandrovna Zentsova, Ulyanovsk State Technical University, graduated from the Faculty of Information Systems and Technologies at Ulyanovsk State Technical University; Postgraduate Student at the Department of Applied Mathematics and Informatics at Ulyanovsk State Technical University; an author of scientific papers in the field of statistical process control. [e-mail: e_zentsova@mail.ru]E. Zentsova

Comparison of parameters optimization approaches of hotteling’s control chart000_7.pdf

Quality of a product produced in a multivariate process is determined by multiple quality characteristics. If each characteristic of a set of correlated characteristics is controlled by an univariate control chart independently, it should lead to wrong conclusions. Unnecessary process stoppage and adjustment as well as incorrect detection of an out-of-control process state are possible. Therefore, the statistical control of a process with correlated quality characteristics should be carried out using multivariate control charts. The most common multivariate statistical tool is a Hotelling’s control chart. It is used for technological process stability monitoring and allows detection of large shifts in the multivariate process settings level. In order to improve detection of small shifts, the implementation of adaptive control schemes with different sets of variable parameters is suggested. The use of these schemes implies tightening control of the process when a sample point on a plot exceeds the warning limit. That contributes to earlier detection of the process mean shift. The set of conditions that must be satisfied to perform a meaningful and unbiased comparison of these schemes is specified. On their basis an optimization problem is formulated. The period between an assignable cause occurrence and detection is used as an objective function. For solving the optimization problem a genetic algorithm is suggested. This study presents a design of six adaptive control schemes. Comparative analysis of their sensitivity for detecting different magnitude of the process shift is performed.

Adaptive control scheme, hotelling’s control chart, markov chain, genetic algorithm.

2017_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.


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