Monitoring general linear profiles using simultaneous confidence sets schemes

• Simultaneous confidence sets based charts for linear profiles monitoring are proposed.
• The EWMA chart for the mean profile takes account of the features of entire profile.
• Simulations show that the proposed chart outperforms the existing one.
• A method is used to find the changepoint and identify the parameters of change.
• An industry example is used to illustrate the proposed chart and diagnostic method.

In this article we consider the quality of a process which can be characterized by a general linear profile. For monitoring the general linear profile, we mimic the charting scheme for the distribution of a univariate quality characteristic by using two individual charts for the mean and variance of the profile, respectively. For monitoring the mean of the profile, based on the concept of simultaneous confidence set we propose a novel exponentially weighted moving average (EWMA) chart, which takes the features of the entire profile into account. Then this chart is used together with an EWMA chart for the variance of the profile to monitor the whole profile. Simulation studies show the effectiveness and efficiency of the proposed monitoring scheme. Furthermore, a systematic diagnostic method in the literature is utilized to find the change point location and to identify the parameters of change in the process. Finally, we use an example from semiconductor manufacturing industry to demonstrate the implementation of the proposed monitoring scheme and diagnostic method.