Process Capability Assessment Under Measurement System Errors: Misclassification Risks and Statistical Feasibility

Measurement system errors can distort product conformity classification and compromise the reconstruction of true process nonconformity, particularly in highly capable manufacturing processes. This study examines when finite measurement system reference information is sufficient to support statistically reliable inverse reconstruction. Experiments involving two micrometers and three tolerance widths (0.200, 0.050, and 0.020 mm) yielded false-rejection probabilities ranging from 1.000 % to 31.968 % and false-acceptance probabilities from 1.833 % to 31.411 %. The results reveal substantial sensitivity to tolerance width, systematic measurement-error shifts, and reference-population composition. Although inverse correction remains algebraically admissible when the classification discrimination factor is positive and the observed fraction satisfies the corresponding bounds, its statistical reliability is constrained by uncertainty in the estimated misclassification probabilities. For highly capable processes, the true nonconforming fraction becomes increasingly small relative to the false-rejection background. Consequently, the probability of satisfying the lower inverse-feasibility condition decreases as true process capability increases and, under normal approximation, approaches a limit determined by the available conforming-reference information, even as production sample size tends to infinity. This study translates established inverse-correction and uncertainty-propagation relationships into decision-oriented reference-information requirements, distinguishing algebraic admissibility from estimation precision and reliable process capability decisions. These findings demonstrate why, under the investigated finite-reference uncertainty model, increasing production sample size alone cannot overcome insufficient measurement system reference information.