2019 AOAC CASP Book

G UIDELINES FOR S TANDARD M ETHOD P ERFORMANCE R EQUIREMENTS

AOAC O FFICIAL M ETHODS OF A NALYSIS (2012)

Appendix F, p. 10

Table A7. POD and number of test portions a,b

Sample size required for proportion

Assume Inference

1. Binary outcome (occur/not occur). 2. Constant probability rho of event occurring. 3. Independent trials (e.g., simple random sample). 4. Fixed number of trials ( N )

95% Confidence interval lies entirely at or above specified minimum rho

Desired

Sample size N needed

1-Sided lower confidence limit on rho c , %

Expected lower confidence limit on rho, %

Expected upper confidence limit on rho, %

Minimum probability rho, %

Minimum No. events ( x )

Maximum No. nonevents ( y )

Effective AOQL d rho, %

Sample size ( N )

50 50 50 50 50 55 55 55 55 55 60 60 60 60 60 65 65 65 65 65 70 70 70 70 70 75 75 75 75 75 80 80 80 80 85 85 85 90 90 90 95 95 95 95 98 98 99 99

3

3 8

0 2 6

52.6 54.1 51.6 52.0 50.8 59.7 65.2 56.8 57.1 55.9 64.9 65.2 62.2 62.4 61.0 68.9 65.2 67.8 65.1 65.0 72.1 78.7 73.8 70.7 70.4 76.9 78.7 80.4 76.5 75.9 80.3 80.4 82.7 80.2 88.1 86.0 86.1 93.7 90.4 91.0 95.7 96.7 95.2 95.5 98.0 98.2 99.0 99.1

43.8 49.0 48.1 49.5 49.0 51.0 59.6 53.1 54.6 54.1 56.5 59.6 58.4 59.8 59.2 61.0 59.6 64.0 62.5 63.2 64.6 72.2 69.9 68.0 68.6 70.1 72.2 76.4 73.9 74.2 74.1 76.4 80.1 78.5 83.9 83.5 84.6 91.2 88.6 89.5 94.0 95.4 94.0 94.3 97.1 97.7 98.6 98.8

100.0

71.9 71.7 66.8 63.7 59.5 75.5 79.8 71.0 68.2 64.3 78.3 79.8 75.2 72.8 69.1 80.5 79.8 79.4 75.1 72.7 82.3 86.1 83.6 79.7 77.4 85.0 86.1 88.2 84.2 82.2 87.1 88.2 88.8 85.8 91.9 91.1 90.6 95.6 93.9 94.1 97.0 97.7 97.0 97.2 98.6 98.8 99.3

10 20 40 80 10 20 40 80 10 20 40 80 10 20 40 80 10 20 40 80 10 20 40 80 11 20 40 80 20 40 80 40 60 80 60 80 90 96 4 5 6 7 9

94.3 85.5 77.9 70.0

14 26 48

14 32

4 9

0 1 5

100.0 100.0

15 28 52

88.8 81.9 74.5

12 28

5 9

0 1 4

100.0 100.0

16 30 56

91.9 85.8 78.9

10 24

6 9

0 1 3 9 0 0 2 7 0 0 1 5 0 1 3 0 2 6 0 2 3 0 0 1 1 0 1 0 1

100.0 100.0

17 31 59 10 18 33 63 10 19 35 67 11 19 37 70 20 38 74 40 58 77 60 80 89 95 7 9

94.8 87.7 82.1

21

100.0 100.0

97.2 91.3 86.3

17

100.0 100.0 100.0

94.5 90.3

13

100.0 100.0

97.4 93.1

10

100.0

98.6 96.5

100.0

99.1 98.7

100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0

130 240 280 480

130 239 280 479

99.4 a Table excerpted from Technical Report TR308, Sampling plans to verify the proportion of an event exceeds or falls below a specified value , LaBudde, R. (June 4, 2010) (not published). The table was produced as part of an informative report for the Working Group for Validation of Identity Methods for Botanical Raw Materials commissioned by the AOAC INTERNATIONAL Presidential Task Force on Dietary Supplements. The project was funded by the Office of Dietary Supplements, National Institutes of Health. b Copyright 2010 by Least Cost Formulations, Ltd. All rights reserved. c Based on modified Wilson score 1-sided confidence interval. d AOQL = Average outgoing quality level.

© 2012 AOAC INTERNATIONAL