Gage Repeatability and Reproducibility Investigations of a Test Rig Using ANOVA/Xbar-R Method

Abstract

In an experimental study, good measurement systems are important for approaching successful decisions. The assessment of a measurement system is known as “Gage Repeatability and Reproducibility” (GR&R). “Measurement System Analysis” (MSA) should be performed at the beginning of an experimental study to ensure that the information to be collected are true representation of what is occurring in the experiment. Experimental data collected under the same condition usually show variation, which arises partly from the experimental system, partly from the measurement devices and partly from the operator who makes the measurements. MSA helps to differentiate the contribution of each source to the randomness of the data. In this way, one may see whether there is a need to reduce the measurement variation so that the data reflects basically the experimental variation. Besides, MSA gives quantitative measures for repeatability and reproducibility. Repeatability is the variation in repeated measurements taken by the same operator under the same experimental conditions. Reproducibility is the variation in data obtained by different operators taking the measurement with the same setup under the same conditions. These are measures of the consistency and precision of the data. GR&R is the most common MSA tool that analyzes the viability of an experimental set-up. Resultant GR&R will indicate overall measurement system variation as the sum of repeatability variation and reproducibility variation. Generally, GR&R % gives a measure of the suitability of the measurement system to yield acceptable data for statistical studies such as “Design Of Experiments” (DOE), “One Factor At a Time” (OFAT), “Response Surface Methodology”, etc. [1, 2]. In this paper, “Analysis of Variance” (ANOVA) and the “Average and Range” (Xbar & R) methods are used to assess the capability of a laboratory made measurement device, which is used for the investigations of a belt drive system efficiency. GR&R is applied at the design stages of the construction of the test rig and final application is presented in this study. The results prove that the test rig is capable of making experimental studies using statistical methods such as DOE and Response Surface Methodology.