Comparing Curves Using Additive Models

Advances in technology have increased dramatically the amount of data measured in industrial processes. Thousands of measurements are available nowadays in operations where previously only a single measurement, at a given point in time or space, was taken. These measurements allow the reconstruction of the whole profile or "signature" of the operation over time or space. Examples are the tonnage applied in a stamping press during a stroke and the density profile of particleboard. Many of these signatures have complicated forms that are not well modeled with parametric models. In this paper, a relatively new class of models called additive models is used to assess the sources of variation active on these signatures. The model contains a nonparametric or smooth portion to model the form of the signature, and a parametric portion to evaluate other sources of variation. An analysis of variance table is developed to test the magnitude of sources of variation. These techniques are illustrated using density profiles of engineered wood boards. Instructions on the implementation of these techniques in S-Plus and SAS are given.