Defect detection via product interaction contrasts

A local manufacturer produces large quantities of cylindrical, ceramic blocks. Every block is X-rayed and examined individually for defects. We have developed a method by which defects can be automatically identified and their significance statistically measured.; There are already a number of image analysis techniques that could possibly identify defects in the images. However, these techniques are typically sensitive to noise in the image, and efforts to remove or reduce the noise from an image can potentially remove the defects as well.; As the images of the blocks are rectangular, we can model non-defective blocks with a two-way additive model. Any unusual patterns in the residuals might indicate the presence of a defect. Examination of the residuals for blocks with obvious defects reveals an interesting pattern. We propose looking for these patterns by way of product interaction contrasts. Data-based and rank-based methods will be discussed, and their asymptotic behavior will be linked to that of linear functions of a Brownian sheet.