Process adjustment is a complimentary tool to process monitoring in process control. Process adjustment directs on maintaining a process output close to a target value by manipulating another controllable variable, by which significant process improvement can be achieved. Therefore, this approach can be applied to the `Improve` stage of Six Sigma strategy. Though the optimal control rule minimizes process variability in general, it may not properly function when special causes occur in underlying process, resulting in off-target bias and increased variability in the adjusted output process, possibly for long periods. In this paper, we consider a responsive feedback control system and the minimum mean square error control rule. The bias in the adjusted output process is investigated in a general framework, especially focussing on stationary underlying process and the special cause of level shift type. Illustrative examples are employed to illustrate the issues discussed.