A Comparative Study of the Performance of Univariate and Multivariate Quality Control Charts in Monitoring the Quality of Milk Products Using Simulated Data

Abstract

This study aims to conduct an applied comparison to evaluate the efficiency of univariate and multivariate statistical process control charts in detecting process deviations and monitoring the quality of production processes. A simulation approach was employed to generate data using the statistical software R, representing the actual characteristics of milk products based on three essential correlated physicochemical variables: fat content, pH value, and density.
The practical part of the study consisted of two stages. In the first stage, statistically controlled data following the normal distribution were generated. In the second stage, artificial shifts in the process means were introduced from sample number 36 to 70 to evaluate the sensitivity of the control charts. The X̄ and R control charts were applied as univariate control charts and compared with Hotelling’s T² and Multivariate Exponentially Weighted Moving Average (MEWMA) charts as multivariate control charts.
The results of the first stage indicated that the production process was statistically stable according to all applied control charts. However, in the second stage (after introducing the shifts), the X̄ charts for fat content and density showed clear points beyond the statistical control limits, while the pH chart did not exceed the control limits but revealed a non-random pattern (a sequence of seven consecutive points). In contrast, the Hotelling’s T² chart successfully detected the process shift by identifying five points beyond the upper control limit. The MEWMA chart showed the earliest and clearest detection of the sudden change, demonstrating a continuous and early shift outside the control limits starting from point 37 until the end of the time series.
The study concludes that multivariate statistical process control charts, particularly the MEWMA chart, provide higher efficiency and accuracy in monitoring modern industrial processes with correlated quality characteristics compared with traditional univariate control charts.