Confidence intervals in repeatability and reproducibility using the Bootstrap method

Abstract

The repeatability and reproducibility (R&R) study--also called a gauge capability study--has been employed as part of the statistical process control program in many organizations. The objective of the study is to determine whether a measurement procedure or instrument is adequate for monitoring the performance of a process. The classical control chart method can be easily performed and calculations can be done with a spreadsheet or statistical computer software. However, this approach only provides the point estimates on the variance components of the measurement error study. In many situations, confidence intervals are more useful than point estimates, because an interval estimate enables an engineer to see both how small and how large an effect may be. In this paper, the Bootstrap method is used for obtaining the confidence intervals of the gauge variability when the control chart method is use for finding the point estimates. One real-life example is used to show the application of this control chart with the Bootstrapping method and comparisons are made with three experimental design procedures in terms of point estimates and confidence intervals for repeatability, reproducibility and total gauge variability.