When an economic-statistical model for a control chart is considered the effect of the choice of the bounds on the average times until a signal on the cost for controlling the process, including the cost with non-conformities produced, and on the design parameters is a natural issue that arises. To have an idea of how the costs and the chart’s parameters are affected by these bounds is an important guidance for the design of the control charts, that is, for the choice of the size of the samples, the intervals between samplings, and the factors used in determining the width of the control limits. A sensitivity analysis of the choice of these bounds on the cost and the design parameters is presented to the adaptive X chart.