The recently manufacturing industry is developing rapidly with the development of various engineering technologies. Accordingly, manufacturing technology and manufacturing management technology are also developing. The most basic manufacturing management technique is Statistical Process Control (SPC). Among the various methods of SPC, the control chart is a method of statistically monitoring the quality characteristics of the process to determine the change of the process. The control chart basically assumes that the quality characteristic values follow a normal distribution. However, if the quality characteristics do not follow a normal distribution, there is a statistical error using the existing control chart method. In this paper, we study the method of designing CUSUM control chart using Box-Cox Transformation method when quality characteristic is non-normal distribution.