This article considers the economic statistical process control for two dependent processes with a failure mechanism which obeys Weibull shock model and has an increasing failure rate. We construct individual economic statistical X control chart to monitor the quality variable produced by the first process, and use the cause-selecting control chart to monitor the specific quality produced by the second process with minimal cost and required statistical properties. By using the proposed control charts, we can effectively and economically distinguish which process is out of control. The renewal theorem approach is extended to construct the cost model for our proposed control charts, and optimization method is used to determine the optimal design parameters of the proposed control charts. Finally, we give an example to show how to construct and apply the proposed control charts. Sensitivity analysis that illustrates the effects of the cost and process parameters on the optimal design parameters and the minimal expected cost per unit time for the proposed control charts is also presented.