Alban Petitjean
The Gauge R&R (Repeatability & Reproducibility) study is a metrological analysis that aims to determine the repeatability and reproducibility of a measurement system. The determination of repeatability and reproducibility is conducted by assuming a random effects model and calculating the variances of the measurements estimated through the Analysis of Variance (ANOVA) method. During a Gauge R&R, certain measurements may distort the ANOVA method or provide redundant information. Reducing the number of measurements can address these issues while simultaneously lowering the cost of the Gauge R&R. To minimize the number of measurements, various optimality criteria such as A, E, and D-optimal designs can be employed. These optimal designs are introduced, utilized, and applied to both simulated data and experimental measurements. This approach enables us to identify the most relevant criterion for a given situation and to assess the impact of reducing the number of measurements on the results obtained during the Gauge R&R study. In general, the D-optimal design primarily maximizes the number of series or parts measured ( ). The A-optimal design and the E-optimal design usually maximize both the number of series ( ) and the number of operators ( ). When the total number of measurements does not allow both and to be maximized simultaneously, A-optimization typically favors a higher number of series ( ) over operators ( ), whereas the E-optimal design tends to do the opposite. Overall, simulations based on synthetic data indicate that it is not necessary to perform three measurements per series; two measurements per series are generally sufficient. When the operator’s influence on the measurement is negligible, these optimal designs enable a reliable Gauge R&R study while reducing the total number of measurements by approximately 64%. An iterative algorithm is also proposed to systematically achieve a reliable Gauge R&R while minimizing the number of measurements required.