The Design of $\overline{\boldsymbol{X}}$ Chart When the Mean and Parameters of Gamma Distribution Change

Control chart technology is one of the important tools in statistical methods and is often used in process control. Some studies assumed the two parameters of gamma distribution are unchanged and changed the mean values to investigated the ability of detecting mean shifts. This study presented a new type of process variation that the two parameters and mean occur change, simultaneously, when the process observations are following a gamma distribution. This study proposed a statistical model to optimize the control chart for monitoring the changes of two parameters and mean. A genetic algorithm was used to solve this model for obtained the optimal design of control chart, and its performance was also investigated. Finally, a real case is used to verify the feasibility of the method in this study.