Determination of optimal experimental design for ANOVA gauge R&R using stochastic programming

Abstract

The ANOVA gauge repeatability and reproducibility study (AGRR) is one of the most popular assessment tools for evaluating the precision of a measurement system. Adequacy of a measurement system critically depends on experimental design, namely, numbers of operators, sampled parts, and replicates. Some previous studies have suggested several rules of thumb and an optimization approach that determine a proper experimental design for AGRR. The usage of those, however, is limited because the procedures are not systematic and a disordered sequence in use exists. This research aims at proposing a systematic procedure to determine the optimal experimental design for AGRR with minimum prior knowledge. To achieve this goal, we adopted the sample average approximation for finding optimal solutions at possible ranges of parameters. Extensive simulation results show that there is a relationship between confidence interval of signal-to-noise ratio and optimal experimental design. Finally, incorporating a regression analysis, we developed a systematic procedure to determine an optimal experimental design before conducting the AGRR.