Monitoring Product Size and Edging from Bivariate Profile Data

Profile data consist of the coordinates of points along the edge of the product. Often, several hundred points are involved. Mechanical and automated procedures (e.g., scanning) are used in data gathering. The large data dimensionality presents challenges in the development of control charts to monitor product profiles. The data also show strong cross-correlations between points close to one another. In this article, using the leading principal components of the coordinate covariance matrix, we develop Hotelling's T2 and upper exponentially weighted moving average (EWMA) charts to monitor product size. The methods are extended to monitor product edging using the angles between the normal vectors of the blueprint and sample profiles. We use a Markov chain approximation to calculate average run length. Through simulations, we assess the performance of the proposed methods and show the upper EWMA chart exhibit good performance in most of the off-target scenarios considered. A comparison with existing methods reveals that the proposed charts are very competitive and require fewer distributional assumptions.