The use of D-optimal design in an expanded gauge R&R study

Abstract

This article evaluates the repeatability and reproducibility of a measurement system with crossed and nested factors. The number of measurements is reduced so that not all measurements are replicated as is usual in R&R experiments. D-optimal design is employed to allocate replicated treatments, and the effect of the reduction is investigated through computer simulation. The analysis is based on a random effects model and the variance components are estimated by the ANOVA method. Recommendations are provided for selecting the number of replicated treatments so that the impact on the precision of estimating the %GRR metric is sufficiently small.

Keywords:

• ANOVA
• D-optimal design
• random-effects model
• repeatability
• reproducibility
• variance components

Additional information

Notes on contributors

Eva Jarosova

Eva Jarosova lectures as an associate professor in the Department of Quantitative Methods at the SKODA AUTO University, Mlada Boleslav, Czech Republic. Previously she worked at the University of Economics in Prague, in the Department of Statistics and Probability, where she was appointed associate professor. She also participates in the work of the Technical Committee TNK4 (Applications of Statistical Methods) in the Czech Standardization Agency. She is a member of the Czech Statistical Society and the Czech Society for Quality.