Gauge R&R: An Effective Methodology for Determining the Adequacy of a New Measurement System for Micron-level Metrology

To compete in a global marketplace, manufacturers are increasingly turning to advanced manufacturing techniques to increase productivity and gain a competitive advantage. This trend requires management to be able to make decisions based on proper quantitative analysis of data. In the manufacturing process, control of variation with an increasingly high degree of precision demands an improved degree of measurement effectiveness. Measurement Systems Analysis (MSA) is a collection of statistical methods (which includes the Gauge Repeatability and Reproducibility study) for the analysis of measurement system capability (Automotive Industry Action Group [AIAG], 2002; Smith, McCrary, & Callahan, 2007)

Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies

We give a short and self-contained proof for rates of convergence of the Allen--Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter exists and starting from well-prepared initial data. Our approach is based on a relative entropy technique. In particular, it does not require a stability analysis for the linearized Allen--Cahn operator. As our analysis also does not rely on the comparison principle, we expect it to be applicable to more complex equations and systems