Nonrepeatable gauge R&R studies assuming temporal or patterned object variation

The standard method to assess a measurement system’s precision is a gauge repeatability and reproducibility (gauge R&R) study. It exploits replications to estimate variance components that are interpreted as measurement spread. For nonrepeatable measurements, it is not feasible to obtain replications because objects are destroyed when they are measured or because the object changes over time. Possible solutions are to replace replications with measurements of multiple objects or with the measurement of one object at multiple times. Subsequently, these measurements are modeled by a fixed pattern (over time or over positions). We show that the experimental design used in this type of nonrepeatable gauge R&R studies is best constructed in a way that is similar to a Latin square design. These designs have a great flexibility, can be applied in many situations encountered in practice, and have nice mathematical properties as well. We consider several examples in which this approach is applied and worked out. For the examples given, we provide the analysis and the results following the worked-out approach. Analysis of the envisaged experimental set-up is done with linear and nonlinear mixed models in which variance components are estimated by restricted maximum-likelihood estimators.