Risk-controlled multi-view industrial anomaly detection: finite-sample false discovery rate guarantees on the Real-IAD benchmark

Industrial anomaly detectors flag suspect parts for human review, yet most report only point-estimate accuracy and no guarantee on the rate of false alarms among flagged parts. We study risk-controlled detection on the Real-IAD multi-view benchmark, where each physical sample is imaged from five cameras. We wrap any multi-view anomaly scorer in a distribution-free calibration layer and control the false discovery rate at the level of physical samples in finite samples. The layer pairs split-conformal p-values with Mondrian stratification by object category and Benjamini-Hochberg selection, and we state the guarantees as propositions, with dependence-robust and adaptive variants. We evaluate the sample-level claims over one hundred resplits. Empirical coverage matches nominal levels, Mondrian calibration removes the worst-stratum miscoverage of pooled calibration, and the false discovery rate is controlled at every level for every scorer we test, while published flow-based detectors run through the same wrapper reach the highest sample-level accuracy and the most guaranteed discoveries. A sizing rule ties the calibration set to the target level, the scorer, and the defect prevalence, and explains why uncorrected thresholds lose control at low prevalence while the wrapper does not. A trimmed p-value keeps validity when the calibration set contains a bounded number of undetected anomalies. A reference batch of verified normals detects damaging drift, recalibration restores control, and the false discovery rate bound survives any fixed image-based category taxonomy when parts arrive unsorted. Pixel-level risk control bounds both error rates of localization masks.