Measurement uncertainty for detection of visual impurities in granular feed and food materials in relation to the investigated amount of material

Figures & data

Figure 1. Images of targeted undesirable substances. Left: Ambrosia artemisiifolia seed surrounded with matrix material, collection of A. artemisiifolia seeds. Right: ergot sclerotia showing size diversity (top) with matrix kernels (rye seeds; bottom). Size bars 5 mm.

Figure 2. Flow chart of the monitoring procedure to establish the correct contamination level of units of undesirable substances in feeds of whole kernels.

Table 1. Geometric mean (GM) and geometric standard deviation (GSD) to characterise lognormal distributions of particle number (in 500 g) and particle weight estimated from available data sets.

Dataset (Number of samples with complete data)	Number of particles per portion	Number of particles per portion	Particle weight (mg)	Particle weight (mg)
	$G{M}_n$	$GS{D}_n$	$G{M}_w$	$GS{D}_w$
Ambrosia seeds (n = 117)	0.7 (0.4–1.2)	5.0 (4.0–5.8)	4.6 (4.3–5.0)	1.4 (1.3–1.5)
Datura seeds (n = 117)	0.3 (0.2–0.5)	4.2 (3.8–4.6)	7.4 (7.2–7.7)	1.2 (1.1–1.2)
Ergot sclerotia (n = 65)	1.2 (0.7–1.9)	3.4 (3.0–3.8)	16.1 (12.6–20.0)	2.6 (2.3–3.1)

Uncertainty distributions of the GM and GSD are expressed by their median value and confidence limits (P5–P95) based on 1000 resampled datasets.

Table 2. Estimated thresholds for screening results (one or two portions).

Target	Legal limit (mg kg^−1)	Threshold (mg kg^−1) Screen one portion	Threshold (mg kg^−1) Screen two portions
Ambrosia seeds	50	23.8 (17.5–28.2)	34.7 (33.2–36.3)
Datura seeds	1000	865 (857–874)	912 (907–918)
Ergot sclerotia, food	200	41 (0–88)	99 (71–123)
Ergot sclerotia, feed	500	294 (230–344)	353 (308–386)
Ergot sclerotia, feed	1000	733 (642–810)	787 (730–830)

Median value and confidence limits (P5–P95) from B resampled datasets (Ambrosia and ergot: B = 1000; Datura: B = 100). Lower uncertainty bounds (P5 values, in bold) are suggested for regulatory use based on the current datasets.

Table 3. Estimated probabilities of false negative results P(FN) for screening one or two portions and using thresholds that are fixed fractions of the legal limit: T = 0.5 × L or T = 0.67 × L.

	Legal limit (L)	P (FN) Screen one portion	P (FN) Screen two portions	P (FN) Screen one portion	P (FN) Screen two portions
Target	(mg kg^−1)	T = 0.5 × L	T = 0.5 × L	T = 0.67 × L	T = 0.67 × L
Ambrosia seeds	50	0.06 (0.04–0.08)	0.011 (0.008–0.015)	0.11 (0.08–0.14)	0.04 (0.03–0.05)
Datura seeds	1000	<0.01	<0.01	<0.01	<0.01
Ergot sclerotia, food	200	0.10 (0.06–0.15)	0.05 (0.03–0.08)	0.14 (0.09–0.20)	0.10 (0.07–0.15)
Ergot sclerotia, feed	500	0.04 (0.02–0.06)	0.013 (0.005–0.027)	0.07 (0.05–0.09)	0.04 (0.02–0.07)
Ergot sclerotia, feed	1000	0.02 (0.01–0.03)	0.004 (0.001–0.011)	0.04 (0.02–0.05)	0.02 (0.01–0.03)

Median value and confidence limits (P5–P95) from B resampled datasets (Ambrosia and ergot: B = 1000; Datura: B = 100). Background shading indicates cases where the upper confidence bound for P(FN) exceeds 0.05.

Figure 3. Flow chart of the bootstrap analysis to establish the analytical thresholds with a probability of 95% correct compliance.

Figure 4. Relative standard deviation in % as a function of correct weight fraction in mg kg⁻¹ for all samples testing positive for Ambrosia.

Figure 5. Relative standard deviation in % as a function of correct weight fraction in mg kg⁻¹ for all samples testing positive for Datura.

Figure 6. Plot of correct weight fractions in mg kg⁻¹ (x-axis) and relative standard deviations in % (y-axis) for all samples of cereals testing positive for ergot sclerotia (dots). The trend line, its equation and correlation coefficient applies to the set of cereal samples.

Figure 7. Fitted logistic curves from example simulated datasets for Ambrosia (L = 50 mg kg⁻¹) and ergot (L = 500 mg kg⁻¹). The horizontal dashed lines are at probabilities 0.05 and 0.5. The vertical dashed lines are at the calculated threshold T and at the legal limit L.

Figure 8. Uncertainty due to number of examined portions is shown in distributions (representing 1000 resampled datasets) of calculated thresholds T for the targets Ambrosia (L = 50 mg kg⁻¹) and ergot (L = 500 mg kg⁻¹) after screening one or two portions. Axis labels indicate maximum T values (in mg kg⁻¹) in each plot.