Monitoring the slopes of linear profiles

Motivated by a vertical density profile problem, in this article we focus on monitoring the slopes of linear profiles. A Shewhart-type control chart for monitoring slopes of linear profiles is proposed. Both Phase I and Phase II applications are discussed. The performance of the proposed chart in Phase I applications is demonstrated using both real-life data in an illustrative example and simulated data in a probability of signal study. For Phase II applications, it is shown that the average run length (ARL) of the proposed control chart depends only on the shifts of slopes, whereas the ARL of the multivariate T² chart depends on both the shifts of slopes and the correlation between the estimated slope and the intercept. When such a correlation is low, the proposed control chart has a better ARL performance than the T² chart.