Using the Monte Carlo Simulation Methods in Gauge Repeatability and Reproducibility of Measurement System Analysis

Abstract

Measurements are required to maintain the consistent quality of all finished and semi-finished products in a production line. Many firms in the automobile and general precision industries apply the TS 16949:2009 Technical Specifications and Measurement System Analysis (MSA) manual to establish measurement systems. This work is undertaken to evaluate gauge repeatability and reproducibility (GR&R) to verify the measuring ability and quality of the measurement frame, as well as to continuously improve and maintain the verification process. Nevertheless, the implementation of GR&R requires considerable time and manpower, and is likely to affect production adversely. In addition, the evaluation value for GR&R is always different owing to the sum of man-made and machine-made variations. Using a Monte Carlo simulation and the prediction of the repeatability and reproducibility of the measurement system analysis, this study aims to determine the distribution of %GR&R and the related number of distinct categories (ndc). This study uses two case studies of an automobile parts manufacturer and the combination of a Monte Carlo simulation, statistical bases, and the prediction of the repeatability and reproducibility of the measurement system analysis to determine the probability density function, the distribution of %GR&R, and the related number of distinct categories (ndc). The method used in this study could evaluate effectively the possible range of the GR&R of the measurement capability, in order to establish a prediction model for the evaluation of the measurement capacity of a measurement system.