On Small Shifts in Quality Control

The Shewhart Xbar chart is effective in detecting large shifts in a process but unable to find moderate shifts. We show that this blind spot allows shifts smaller than one standard deviation to continue undetected for long periods, thereby incurring much larger total costs than do rapidly detected large shifts. Augmenting the Shewhart chart with a cumulative sum chart largely plugs this gap, leading to much more effective process monitoring.