On the monitoring of mixture simple linear profiles

In some applications, the quality of a process or product is best characterized by a functional relationship between a response variable and one or more explanatory variables. Profile monitoring is used to understand and to check the stability of this relationship or curve over time. In the existing simple linear regression profile models, it is often assumed that the data follow a single mode distribution and consequently the noise of the functional relationship follows a normal distribution. However, in some applications, it is likely that the data may follow a multiple-modes distribution. In this case, it is more appropriate to assume that the data follow a mixture profile. In this study, we focus on a mixture simple linear profile model, and propose new control schemes for Phase II monitoring. The proposed methods are shown to have good performance in a simulation study.