An effective non‐restarting control chart based on the joint judgment

Abstract The cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been widely used in industry and public health applications. Still, few researchers have paid attention to the practical problem in public health applications, in which the control chart statistic cannot be reset to zero after an out‐of‐control (OC) signal. Some studies have addressed this issue by adding an upper limit to the statistic or using adaptive hypothesis testing (AHT). However, the control chart with an upper limit added to the testing statistic leads to a loss of information, and the post‐outbreak false alarm rate is still higher than the restarting control chart. The AHT control charts could not quickly alarm for the pandemic outbreak alarm as expected. To improve these drawbacks of control chart monitoring, two phase‐II non‐restarting (NR) CUSUM–EWMA control charts with the AHT framework, named NR–CUSUM–EWMA and AHUTNR–CUSUM–EWMA control charts, are proposed to well alarm for the pandemic outbreak. The AHTUNR–CUSUM–EWMA control chart uses the joint judgment of the UNR–CUSUM–EWMA (uncorrected NR–CUMSUM–EWMA) and NR–CUSUM–EWMA control charts, and the run rule to enhance the efficiency of the pandemic outbreak alarm. Simulation results show that the proposed NR–CUSUM–EWMA and AHUTNR–CUSUM–EWMA control charts can well maintain the outbreak alarm rate and post‐outbreak false alarm rate without losing cumulative information. Finally, the applicability and effectiveness of the proposed method are illustrated by an application to measles surveillance in North Rhine‐Westphalia, Germany.