- Profile Monitoring

In the SPC problems discussed in the previous chapters, the quality of a product is

characterized by one or more variables. Each sampled product has a single obser-

vation of the quality characteristic variable, and we monitor the related production

process using all available observations of the products sampled over time. In some

applications, however, the quality of a product is characterized by the functional rela-

tionship between a response variable and one or more explanatory variables. In these

applications, for each sampled product, one observes a set of data points of these

variables that can be represented by a curve/surface (or a profile), and the major pur-

pose of SPC is to check the stability of this relationship over time based on observed

profile data. This SPC problem is called profile monitoring in the literature, which is

the main topic of this chapter.