Interval Estimation for Mean Response in a Simple Nested Error Regression Model in Gauge R & R Study

Abstract

In a measurement system monitoring manufacturing processes, one often uses gauge repeatability and reproducibility (R & R) experiment to determine the amount of variability due to parts, final products, operators, or gauge. A measurement system that employs operators randomly chosen to conduct measurements on randomly selected parts can be statistically modelled. When a measurement is assumed to be linearly related to a predictor variable and a simple nested error regression model is applied for the measurement system, one might be interested in making inferences concerning the variability for the mean response in the model. In general, confidence intervals are uniformly more informative than hypothesis tests in making inferences to parametric values in statistical models. Confidence intervals for the mean response in a simple nested error regression model can be useful tools to determine whether the variability is appropriately managed in a manufacturing process. Several confidence intervals for the mean response in the model are proposed. The confidence intervals proposed in this article are based on a moderate large sample method. Computer simulation is performed to see if the proposed intervals maintain the stated confidence level and a numerical example is provided to explain the proposed intervals by calculating confidence intervals for the mean response in the model.