In many applications, the quality of a process is characterized by the functional relationship between a response variable and one or more explanatory variables. This functional relationship is referred to as a profile. We extend two existing methods for monitoring the shift of slope of linear profiles. We consider the single sampling (SS) and the double sampling (DS) scheme for the economic-statistical design (ESD) model of profile monitoring in Phase II. The results of a numerical example indicate the DS ˆ β1 control chart has better performance than the DS T2 control chart when ρ ˆ β0, ˆ β1 is low. Comparison of the ESD of DS ˆ β1 and the SD of DS ˆ β1 control charts show that an ESD has an improvement over the pure SD. Also, we compare the ESD of the DS ˆ β1 with the ESD of the SS ˆ β1 control chart. The results show that the DS ˆ β1 control charts are more efficient in terms of minimizing the E(L).

Keywords