An Analysis of Four Spectral Control Charts

Control charts are used in manufacturing settings to monitor and detect changes in a process. Spectral control charts, based on the periodogram evaluated at the Fourier frequencies, have been designed to detect the onset of periodic behavior. In this article, two additional spectral charts formed using established periodogram tests are proposed. Comparisons of the average run lengths of the spectral charts based on these tests are made using Monte Carlo techniques. These comparisons evaluate how well the methods detect both simple and compound periodic behavior corresponding to both Fourier and non-Fourier frequencies. The charts are also compared using an industrial data set involving the widths of coating on silicon wafers. The analysis will illustrate both the strengths and weaknesses of each procedure and give suggestions as to appropriate usage.