Multivariate quality control is an important tool in statistical quality control, which aims to provide a method for simultaneously controlling multiple correlated variables. One of these methods for detecting out-of-control points in a multivariate quality control process is the use of Hotelling's T2 statistic. The distributional properties of this statistic depend on whether the population parameters are known or unknown, as well as the sampling time, so that depending on these conditions, it has a chi-square, F, or beta sampling distribution. Under certain conditions, the control limits obtained on the basis of these distributions become close to each other and become close to each other. In this article, we discuss the distributional properties of the relationship between them for different process conditions and explain their application in the statistical control process with several real data groups.