Joint X¯ and R charts with variable parameters

Abstract

Recent studies have shown that the X¯ chart with variable parameters (Vp X¯ chart) detects process shifts faster than the traditional X¯ chart. This article extends these studies for processes that are monitored by both, X¯ and R charts. Basically, the X¯ and R values establish if the control should or should not be relaxed. When the X¯ 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.