Theory of Sampling

Guide to Quality Sample Processing

Jo Marie Cook NACRW 2015

2011 Food Safety Modernization Act

• Integrated Food Safety System ▫ Section 202(a)(6): Standards for Sampling and Testing

• Partnership for Food Protection Uniformity in sample collection and “laboratory preparation” is essential…

Harmonized policies and procedures for sample collection, shipment, analysis, storage and retention of food and feed materials ▫ Achieve Data Equivalency

▫ Estimate Overall Error

Goal of Sampling Make a decision about a unit of material based on

analytical data derived from a small mass extracted from the DECISION UNIT

Lab Sampling : Size Reduction to obtain test sample

Question: What is the smallest test sample size?

Theory – Pierre Gy • Compositional Heterogeneity Leads to Fundamental Error • Distributional Heterogeneity Leads to Grouping and Segregation Error

• Sample Correctness and Tools

Compositional Heterogeneity

• Fundamental Error • Collect sufficient mass to represent all the

particles of varying composition ▫ d = Diameter of largest particle ▫ m = Mass of sample collected ▫ C = constant unique to material and analyte

s2(FE) = Cd3 / m

Collect the appropriate mass or reduce the particle size!

Fundamental Error Constant

C = cBfg c = constitution factor: concentration of analyte in critical

particles and density of critical particles B = liberation factor: extent critical particles are liberated f = shape factor: cube = 1, sphere = 0.524, wafer = 0.1 g = size range: uniform = 1, large distribution = 0.25

Distributional Heterogeneity • Grouping and Segregation Error • Assure equal likelihood for all increments

of the lot to be selected • Collect a sufficient number of random

increments

Mix and/or collect many increments!

Sample Correctness • Does your sample contain all of the particles of interest

in your decision unit?

• Eliminate bias generating errors

Theory of Sampling and Measurement Uncertainty

• TOS focuses on the Sampling Process • TOS minimizes all sampling contributions to MU • If the sampling error effects not reduced the MU

estimates are compromised Esbensen and Wagner, Analytical Scientist, 2014

• Eurachem/CITAC Guide: “Measurement Uncertainty Arising from Sampling”, 2007

• DS-3077, “Representative Sampling – Horizontal Standard”, 2013

Survey of Current Lab Practices

• Mix, chop, blend all subs to make a composite

• Vertical cutter/mixer >>

• Cryoprep?

Not homogenous!

Repeat analyses from processed samples

Method Analytical Sample (g)

% Absolute Difference +/- std. dev.

Number

FL Method 50 g 18% +/- 15% 149 QuEChERS 15g 18% +/- 16% 234

QuEChERS 26 Commodities 42 Pesticides

234 F & V - QuEChERS, 15g

0 10 20 30 40 50 60 70 80 90

100

0.01 0.10 1.00 10.00 100.00

Mean Concentration (ppm)

% Absolute Difference vs Concentration

% Diff

% Difference by Pesticide Analyte % n

Acephate 19 6

Captan 25 7

Carbendazim 10 10

Chlorothalonil 22 15

Cypermethrin 34 12

Dinotefuran 20 9

Endosulfan Sulfate 17 17

Iprodione 27 6

Methamidophos 11 6

Prochloraz 16 6

Thophanate Me 13 12

% Difference by Commodity Commodity % n Green beans 0.17 18

Cabbage 0.22 6

Cilantro 0.19 12

Cucumbers 0.18 12

Culantro 0.14 8

Ginger 0.24 7

Malanga 0.19 11

Mint 0.24 6

Papaya 0.15 8

Snap Peas 0.28 6

Peppers, hot 0.29 11

Summer Squash 0.12 13

Strawberry 0.15 13

Thyme 0.24 8

Processing Repeatability – PDP Peaches

• 9 samples of the same commodity with similar detections

• Peaches frequently always have detections • Peaches can be problematic during the

homogenization process and is a commodity that is not peeled

• Original batch extracted- 2/11/15 • Re-extracted - 3/12/15

Temperature of Peaches after Homogenization

Analyst ⁰C after homogenization

John Doe 16.6 Jane Doe 15.9 Bob Doe 17.2

Note: Peaches are stored at ~ 4 ⁰C prior to processing

Peaches Repeatability = 7% +/- 6%

0

5

10

15

20

25

30

0.001 0.01 0.1 1 10

% D

iffe

renc

e

Mean Concentration (ppm)

% diff

Methoxyfenozide (0.017 Original & 0.022 re-extraction)

PDP Peaches Repeatability Analyte % diff n

ACETAMIPRID 10 6 BUPROFEZIN 0 2 CHLORANTRANILIPROLE 23 2 CYHALOTHRIN TOTAL 13 2 CYPRODINIL 0 2 FLUDIOXONIL 7 6 IMAZALIL 2 2 IPRODIONE 4 10 METHOXYFENOZIDE 10 4 PROPICONAZOLE 0 3 PYRIMETHANIL 8 6 SPIRODICLOFEN 8 6 TEBUCONAZOLE 5 8

TOS Sample Processing Quality Criteria • Definition: Size reduction to obtain test sample • Goal: Represent the Decision Unit • Small fundamental, grouping & segregation errors: Appropriate mass Appropriate # of Increments • Sample Correctness: Every particle has the same probability of selection Appropriate tools, procedures • Unbiased • QC to Assess Representativeness = replicates

Minimum Analytical Sample Size?

• Particle size • Size Distribution • Contaminant Level • Contaminant Distribution • Analyte interaction with the matrix • Cross Contamination • Competing Contaminants

Minimum Analytical Sample Size?

M = 10 * λ*d3 E2

M = Mass of sample in grams λ = Density in g/cm3

d3 = diameter of largest particles in cm

E = Tolerable error (0.15 = 15%)

Caution! This assumes a constant of 10.

Your constant may be very different.

“Guidelines for Preparing Laboratory Samples”, AAFCO.org

Cryogenic Blending Minimum Analytical Sample Size?

M = 10 * λ*d3

E2

M = 0.0055 g (Only an Estimate!) λ = 0.8 d3 = 0.0000156 (250 µm)

E = 0.0225 (0.15 = 15%)

Room Temperature vs Freeze & Blend

Do we need Cryogenic Milling for Oranges?

▫ Smaller particle size, mm -> 45 – 250 um (Advantage) ▫ Samples are kept Frozen (Advantage for heat sensitive compounds) ▫Very time consuming (Disadvantage) ▫ Is it fit for purpose?

Room Temperature Blending Oranges

2.46 x 2.06 mm

Microscopy: E.R. Noche

Blending of -80°C Oranges

Still a few large

chunks

Thawing -80°C Blended Oranges

0 sec 10 sec

30 sec 240 sec

0 sec

235 sec

2.22 mm

Thawing -80°C Blended Grapefruit

0 sec

527 sec

230 sec

-80°C Blended Valencia 0.94 x 1.51 mm

1.36 mm

4.85 mm

85 sec.

Repeat Analyses (ppb) - Orange Date 1/29 4/24 4/24 4/24 Subs S1 S3 S3 S3

Frozen cup 1

Frozen cup 3

Frozen cup 3

Frozen cup 3

Penillic Acid (ppb)

504

261

302

308

Penilloic Acid (ppb)

594

425

504

595

*S2 was used for qualitative confirmation of original result

Repeat Analyses (ppb) - Grapefruit Date 3/17 4/24 4/24 4/24 Subs S1 S2 S3 S4

original Frozen cup 2 Frozen cup 3 Resample/blend

Penillic Acid (ppb)

6.8 4.6 5.3 21

Penilloic Acid (ppb)

14 12 14 28

March/April 2015, Open Access

Special Issue – 13 Papers on Theory of Sampling http://aoac.publisher.ingentaconnect.com/content/aoac/jaoac

TOS Forum http://www.impublications.com/tos-forum

Theory of Sampling

Guide to Quality Sample Processing

Questions?