Assessment of a Measurement System Using Repeat Measurements of Failing Units

ABSTRACT

Inspection systems measure every part produced. If the measurement is outside of the inspection limits, then that part is measured again. To assess the quality of these measurement systems, traditionally gauge repeatability and reproducibility (R&R) studies are preformed. Instead of performing a gauge R&R study, we present a method of assessing these measurement systems with operational data from an inspection system. Using the inspection data, we provide a justification for the pooled variance of the measured values for each part that has two measurements. The bias and variance of this analysis of variance (ANOVA) estimator are derived using properties of the truncated normal distribution. We show that the ANOVA estimator has a relatively small bias and high efficiency when compared with the maximum likelihood estimator for most common values of γ or GRR%, which is the measurement system standard deviation divided by total inspection system standard deviation.

KEYWORDS:

• gauge repeatability
• inspection system
• measurement system assessment
• reproducibility study

ACKNOWLEDGMENTS

Ryan Browne acknowledges the financial support of the National Science and Engineering Research Council of Canada (NSERC), Research in Motion Limited, and the Mathematics of Information Technology and Complex Systems (MITACS). We thank the Editor (for the example in testing flammability of plastics and other chemically based products) and the referees for numerous suggestions that greatly improved the article.