ON THE ISSUE OF OPTIMIZATION OF THE PARAMETERS OF MULTIVARIATE STATISTICAL PROCESS CONTROL
Vladimir N. Klyachkin, Victoria O. Tashnichenko · Reliability and Quality of Complex Systems · 2024
Background. Statistical control of processes is designed to identify special (non-random) causes of violation in order to prevent a decrease in the quality of products. Solving optimization problems for different situations and different types of control charts will generally give completely different values for the instantaneous sample size, sampling rate, and control boundary positions. What values should be taken? An urgent problem of multi-criteria optimization arises. Materials and methods. For uncorrelated measures, standard maps of averages and standard deviations or ranges are used. If the correlations between the indicators are significant, special multivariate methods are used, based on the Hotelling algorithm to control the average level of the process and the generalized dispersion algorithm to control scattering. The problem of optimizing control parameters was solved by A. Duncan for Shewhart maps. Later, the problems of optimizing the parameters of the Hotelling algorithms and generalized variance were considered. Results and conclusions. An example of analyzing the stability of the power amplifier unit operation is considered. The solution of the optimization problem made it possible to find the optimal sample size, the interval between samples, the probability of a false alarm and the average time of the process being in an unstable state. A new scientific problem of optimizing the parameters of multivariate statistical process control is formulated. A solution for a specific example is found. In general, when it is necessary to take into account the possibility of different types of violations for different indicators, the problem of multi-criteria optimization is solved.