A Comprehensive Framework for Statistical Inference in Measurement System Assessment Studies

Measurement system analysis aims to quantify the variability in data attributable to the measurement system and evaluate its contribution to overall data variability. This paper conducts a rigorous theoretical investigation of the statistical methods used in such analyses, focusing on variance components and other critical parameters. While established techniques exist for single-variable cases, a systematic theoretical exploration of their properties has been largely overlooked. This study addresses this gap by examining estimators for variance components and other key parameters in measurement system assessment, analyzing their statistical properties, and providing new insights into their reliability, performance, and applicability.