To determine the economic design of control charts and the specification limits with minimum cost are two separate issues in previous research areas. In this study, we proposed a method to determine the optimal design parameters of X control charts and the specification limits simultaneously from an economic viewpoint. We also consider two types of X control charts: one is the economic X control chart and the other is the economic statistical X control chart. We obtain the optimal results by minimizing the expected cost per unit time for the-larger-the-better quality characteristic with a Weibull distribution. We consider the asymmetric control limits because of the asymmetric feature of theWeibull distribution. Also, we are considering the difference between monitoring the process by using an economic statistical X control chart and conducting a complete inspection plan. Which way is better, process control or inspection plan? In our data analysis of the two types of X control chart, we find that the optimal expected cost per unit time with complete inspection is lower than without complete inspection. This is because the coefficient of Taguchi’s quadratic loss function we set is too small. And the analysis shows us the significant parameters for the optimal expected cost per unit time and design parameters. At last, in our numerical examples for two different types of X control chart, we find that the performance of the economic X control chart is as good as the economic statistical one. However, we suggest the producer use the economic statistical X control chart with a complete inspection plan to obtain a lower expected cost per unit time and larger power of the control chart.