Phase II statistical process control for functional data

Abstract

In the manufacturing process, a sequence of measurements of quality characteristic is increasingly taken across some continuum, producing a curve that represents the quality of the item. This curve provides the so-called profile or functional data. Regardless of a linear or nonlinear profile, the common approaches of the control chart are based on the multivariate control chart by monitoring the estimated parameter of the pre-defined linear or nonlinear model. Usually, the model is difficult to know practically, and it is also difficult to identify the abnormal pattern from the outlying parameter. The functional data control chart we propose can provide a better solution to these problems. In the Monte-Carlo simulations, we show that the functional data control chart is sensitive when the underlying process status is changed. By applying the vertical density profile data, the new method exhibits a good performance.

Keywords:

• bootstrap
• control charts
• functional data analysis
• profile