Cusum charts for preliminary analysis of individual observations

A preliminary Cusum chart based on individual observations is developed from the uniformly most powerful test for the detection of linear trends. This Cusum chart is compared with several of its competitors which are based on the likelihood ratio test and on transformations of standardized recursive residuals on which for instance the Q-chart methodology is based. It turns out that the new proposed Cusum chart is not only superior in the detection of linear trend out-of-control conditions, but also in the detection of other out-of-control situations. Approximate control limits, determined from simulation, and an example of its use in practice are given for the proposed Cusum chart.