Vertical Density Profile Monitoring using Mixed-Effects Model

Profile monitoring is a recent field of research in Statistical Process Control (SPC) literature, which is attracting the interests of many researchers. This approach is used where process data follow a profile and the stability of this functional relationship is checked over time. We consider nonparametric mixed effect models for functional data to model the profile. Then, multivariate control charting is applied to identify mean shifts or shape changes in the profile. A real case study dealing with density measurements along the particleboard thickness (usually referred to as Vertical Density Profile -VDP) is taken as reference throughout the paper. Performance of the nonparametric approach is computed for a set of out-of-control scenarios. Our main conclusion is that nonparametric methods represent a flexible and effective solution to complex profile monitoring.