Joint X-bar and R charts with variable parameters

Recent studies have shown that the X-bar chart with variable parameters (Vp X-bar chart) detects process shifts faster than the traditional X-bar chart. This article extends these studies for processes that are monitored by both X-bar and R charts. Basically, the X-bar and R values establish if the control should or should not be relaxed. When the X-bar and R values fall in the central region the control is relaxed because one will wait more to take the next sample and/or the next sample will be smaller than usual. When the X or R values fall in the warning region the control is tightened because one will wait less to take the next sample and the next sample will be larger than usual. The action limits are also made variable. This paper proposes to draw the action limits (for both charts) wider than usual when the control is relaxed and narrower than usual when the control is tightened. The Vp feature improves the joint X and R control chart performance in terms of the speed with which the process mean and/or variance shifts are detected.