The purpose of this research is to develop a statistical method to monitor the fairness of network resource distribution. The newly developed fairness score function allows users to have the same or different priority levels. Especially, this function possesses all the necessary properties required as a quality characteristic for the purpose of statistical process control. The main objective is to find the critical values for the statistical test. Monte Carlo simulation is used to find the critical values. When the users have the same priority level, a table of the critical values is given for different sample sizes and different significance levels. When the users have different priority levels, it is difficult to generate a similar table since the users’ priority levels vary. Therefore, the critical values are computed for given priority levels. In both cases, an example is given to demonstrate the approach developed in this study.