Established Control Limits

The control limits are statistically defined as 3 standard deviations above and below the mean of the data sampled.  In the case of the X-bar chart, the UCL/LCL is 3 STD DEV above/below the average of the sub-groups of the data.
To answer your question (I think) you would always use the UCL/LCL on the chart where it appears.  It exists to determine when a process is statistically in or out of control, not whether the process is meeting specification limits.  The specification limits are set by the customer.
Bottom line, is you use the UCL/LCL to determine statistical control on a process.  Use the specification limits (customer requirements) to determine whether the process is meeting customer expectations.
I hope that this helps. 
Jim

The choice of chart is dependent on the quantity and type of data. Ten data points plotted on a chart (this may be ten sub-group means and ranges or ten single readings) give a reasonable indication of the state of the process. Fifteen to twenty give a strong indication and 25 to 50 is ideal. It gets more complicated if the process is, or appears to be, out of control, since data values due to special causes need to be eliminated before you can calculate the true underlying mean value and the degree of natural variation. Always remember that if you use control charts to monitor processes, you always know much more about the process than someone who doesn’t !