Control chart based on likelihood ratio for monitoring linear profiles

A control chart based on the likelihood ratio is proposed for monitoring the linear profiles. The new chart which integrates the EWMA procedure can detect shifts in either the intercept or the slope or the standard deviation, or shifts simultaneously by a single chart, which is different from other control charts in literature for linear profiles. The results by Monte Carlo simulation show that our approach has good performance across a wide range of possible shifts. We show that the new method has competitive performance relative to other methods in literature in terms of ARL and another feature of the new chart is that it can be easily designed. The application of our proposed method is illustrated by a real data example from an optical imaging system.