A bootstrap method for the measurement error estimation in Gauge R&R Studies

A measurement system fit for use is an essential resource to perform quality control activities: its assessment must be carried out periodically to quantify its bias(location) and precision(width) error to qualify it for the purpose it is used. In particular, the measurement system capability must be determined to evaluate how much of the observed variability originates from the gauge's precision error. Gauge Repeatability and Reproducibility (R&R$R{\&}R$) studies are aimed at getting a reliable estimate of the precision error sigma M$\sigma _M$ of the measurement system. The outcome of a Gauge R&R$R{\&}R$ study are point estimates and confidence intervals of the precision error components and related measurement capability metrics. Here, a general bootstrap-based procedure is proposed to get confidence interval estimations of the measurement error and its components from a Gauge (R&R$R{\&}R$) study for continuous observations carried out with either the Average and Range (ARGG) control chart or the experimental design method. An application of the proposed bootstrap-method is presented for a dataset of observations.