Optimization of multivariate statistical control of scattering technological process indicators

The paper investigates the stability control of a multiparameter technological process when many indicators of this process are monitored at certain intervals. A generalized variance algorithm is used when monitoring the scattering of correlated indicators. The paper proposes an approach related to the search for optimal parameters of this algorithm according to the criterion of the minimum cost associated with control. In order to monitor the stability of process indicators and identify violations to adjust the process timely, we use statistical control – a widespread method of diagnosing and controlling technological processes. When controlling a multiparameter process, some of its indicators are correlated. In this case, Hotelling charts are used to control the average level, and the generalized dispersion algorithm is used to control multivariate scattering. To minimize the parameters of the generalized variance algorithm, three numerical optimization methods are used. The program is written in Python. The paper proposes a methodology and develops an appropriate program for optimizing the parameters of multivariate statistical control of process scattering according to the criterion of minimiz-ing the costs associated with control: the frequency of sampling (the interval between samples), the sample size and the position of the control boundaries. This technique is illustrated by the example of data from a specific technological process: numerical values of control parameters and expected costs are obtained. Multivariate statistical control is used both to monitor the stability of technological processes (for example, machining processes, drug production processes, quality control of drinking water purification), and to diagnose the functioning of systems for various purposes (for example, vibrations of a hydraulic unit). This explains the relevance and practical significance of the research related to its optimization.