Understanding the uses, and limitations, of attributes ......Microorganisms in Foods,...

transcript

Understanding the uses, and

limitations, of attributes sampling

Tom Ross

Food Safety Centre, University of Tasmania and

International Commission on Microbiological Specifications for Foods

Overview

• attributes sampling plans

• statistics of sampling plans

• limitations of testing

• other complications

• sources of advice on sampling and sampling plan

design

Sampling plans

• “attributes” plans

– “2 class” or “3 class”

– test against a (probability of a) specific level of the hazard

– used by buyers, regulators

• “variables” plans

– incorporate all measured levels of the hazard to assess compliance

– must know mean and standard deviation of hazard levels, i.e. a history of quantitative results

“attributes” sampling plans:

• intended to tell what proportion of the units in

the lot meet some criterion (i.e., the

“attribute” we are interested in)

• how many are “acceptable”; how many “pass”,

or “fail”

attributes sampling plans

defined by three (or four) quantities:

• ’m’ – the microbiological limit (e.g., <1 per 25g, 100 cfu/g) desired (= the “attribute”)

– may implicitly dictate the sample size

• ‘n’= the number of samples from the lot that must be tested

• ‘c’ = the number of samples that may exceed ‘m’

• ‘M’ – applied in some cases to recognise occasional deviations, a level higher than ‘m’ but one which must never be exceeded

2 and 3-class attributes plans

2 class:

the criterion is absolute, sample units either “pass” or “fail”

described only by m, c, n

3 class:

the criterion includes a third category, i.e., “marginally acceptable (“M”)

described by M, m, c, n

log count / g

tive p

its in

log count / g

tive p

its in

Two- and three-class attributes plan m m

2-class plan 3-class plan M

acceptable

unacceptable

acceptable

unacceptable

marginally acceptable

Wrong!

In fact, we can never demonstrate ‘zero tolerance’, only a

certain level of confidence that the contamination is

below a certain level

Common Misconception about

Presence/Absence Testing

“If the test is negative, the batch is free from

pathogens”

Sampling and the Probability of Detection

<50% defective?

<10% defective?

<1 % defective?

Sampling and the Probability of

Detection

• probability of detection depends on

– actual proportion of samples that are unacceptable

– number of samples examined

– it is easily described mathematically (a binomial sampling process)

- (in fact, the ‘hypergeometric’ distribution is more correct, but for low contamination values, the results are nearly equivalent)

Pacceptance = (1 - Pdefective)number of samples examined

Binomial Distribution

• Pacceptance often = 0.05 (i.e., 95% confidence that a ‘bad’

batch will be detected and rejected

• Pdefective = real proportion defective or the upper limit of

our tolerance of units that don’t meet our criterion

Pacceptance = (1 - Pdefective)number of samples examined

“attributes” sampling plans

confidence in the result of testing is based on:

– number of samples taken

– true (or required) frequency of compliance

plan performance (confidence) is summarised as

‘operating characteristic curve’

0 0.2 0.4 0.6 0.8 1

Proportion defective sample units in a lot

Operating Characteristic Curve

(n=5, c=0)

Probability of accepting a lot (Operating Characteristic Curves)

0 0.2 0.4 0.6 0.8 1

Proportion defective sample units in a lot

Probability of acceptance with 5 negative

samples depends in true ‘defect’ rate

Pacceptance = 0.05 with 5 samples (all negative); depends on true ‘defect’ rate

n = 5, c = 0

• means that we can be 95% confident only that, on

average, less than half the units in the lot exceed

the ‘attribute’, m.

0.05 = (1 - Pdefective) 5

=> Pdefective = 0.46

what’s acceptable (“appropriate level of protection”)

• 50 % defective (=contaminated)?

• 1 % contaminated?

• 0.1% contaminated?

• 0.01% contaminated (1 in 10,000 chance)?

samples required for 95% confidence of rejection of a non-compliant lot

• no sampling plan can ever guarantee absolute safety of the food

• the sampling plan can only provide a certain level of confidence

• it is virtually* impossible to use sampling and testing to determine whether a lot of product is acceptable when the tolerable level of failure is very low, or zero

• better to rely on preventive approaches

Limitations of Testing

• methods may not recover injured cells

• microbiological condition of the food changes over time

• microbial contamination isn’t uniformly distributed

throughout the lot

• even if microbes were completely evenly distributed the

samples would not contain identical numbers of cells

• microbial contamination isn’t uniformly distributed

throughout the lot

• even if microbes were completely evenly distributed the

samples would not contain identical numbers of cells

Variability and acceptable levels

• microoorganisms aren’t uniformly distributed throughout the lot

• even if they were completely evenly distributed the samples would

not contain identical numbers of cells

Poisson processes

• random sampling from a population when assessing

a (binomial) attribute is a Poisson process

• the chances of making a particular number of

observations, in a given time, or space, based on

some true average density, or frequency, is defined

by the Poisson distribution

• for example….

• if the concentration of a pathogen in a food:

– were exactly 1 cell per cm3, and

– the cells were perfectly evenly distributed, and

– our sample size was exactly one cm3

• our samples of 1 cm3 would not always contain 1

cell….

Poisson processes

Poisson sampling “error”

i.e., mean concentration is one cell per sample unit

i.e. but a sample could, by chance, contain four

cells …

Poisson sampling “error”

or could contain two cells …

Poisson distribution

• The probability that a certain number of ‘events’

(e.g., number of positive samples) will be observed,

when the true average of those ‘events’ is known, is

given as:

P(observing n positives) =

(true_averagen ) ´ e-( true _ average )

ICMSF Sampling Plans – ‘risk’ basis

everity

increasing probability of unacceptable hazard

Examples of Sampling Plans

ICMSF: Microorganisms in Foods, 2. Sampling for Microbiological Analysis. Principles and Specific Applications,

2nd Edition, Blackwell Scientific Publications, 1986 (ISBN-0632-015-675).

Advice on Sampling Plan Design and Interpretation (http://www.icmsf.org)

Attributes Sampling Plans

• are like the results of MPN tests

• if we can quantify, or estimate, the variability of

contamination levels in a lot, we can calculate the

sensitivity and confidence of the sampling plan

using the equations and understanding just

presented

• its complicated!

Food Control, 20 (2009): 967 - 979

ICMSF Sampling Plan Spreadsheet (www. icmsf.org)

Conclusions

• in the absence of non-destructive testing, we can never

guarantee that a lot contains no unacceptable units

• transparent, science-based criteria and sampling plans

can be developed and their performance compared based

on knowledge of the SD of contamination within a lot

• correct design, and interpretation, of sampling plans is

complex

• user-friendly tools are available, for free, to assist

Useful Reading

van Schothorst, M., Zwietering, M.H., Ross, T., Buchanan, R.L and Cole, M.B. International

Commission on Microbiological Specifications for Foods. (2009). Relating

microbiological criteria to food safety objectives and performance objectives. Food

Control, 20: 967-979.ICMSF

R.C. Whiting, A. Rainosek, R.L. Buchanan, M. Milioti, D. LaBarre, W. Long, A. Ruple and S.

Schaub. (2006). Determining the microbiological criteria for lot rejection from the

performance objective or food safety objective. International Journal of Food

Microbiology, 110: 263–267.

ICMSF (International Commission on Microbiological Specifications for Foods), 2002.

Microorganisms in Foods, Microbiological Testing in Food Safety Management, Vol. 7.

Kluwer Academic/Plenum Pub, NY. 362 pp.

Acknowledgements

SAAFoST

International Commission on Microbiological

Specifications of Foods

Understanding the uses, and limitations, of attributes ......Microorganisms in Foods,...

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