CUSUM charts for preliminary analysis of individual observations

A preliminary cumulative sum (CUSUM) chart based on individual observations is developed from the uniformly most powerful test for the detection of li near trends. This CUSUM chart is compared with several of its alternatives which are based on the likelihood ratio test and on transformations of stan dardized recursive residuals on which, for instance, the Q-chart methodolog y is based. It turns out that the proposed CUSUM chart is not only superior in the detection of linear trend out-of-control conditions. but also in th e detection of other out-of-control situations considered in this paper. Ap proximate control limits, determined from simulation and an example of its use in practice are given for the proposed CUSUM chart.