As the number of samples tested increases, so does our confidence in the
result but so too does the cost of testing. To be sure of the quality of the
batch or lot we would have to test it all, but since microbiological testing is
destructive, this would result in almost absolute confidence in the product
quality but none left to sell. A compromise must therefore be struck
between what is practicable and what gives the best estimate of lot quality.
11.2 Sampling Schemes
The sampling scheme most commonly applied in the microbiological
testing of foods is that of sampling for attributes. It makes no assump-
tion about the distribution of micro-organisms within the batch of food
and is therefore particularly suited to situations where we have no
knowledge of this; for example with imported foods at their port of entry.
11.2.1 Two-class Attributes Plans
In an attributes sampling scheme analytical results are assigned into
classes; in the simplest type, the two-class scheme, samples are classified
as acceptable or defective depending on the test result. A sample is
described as defective if it is shown to contain more than a specified
number of organisms or, in cases where a presence or absence test is
applied, the target organism is detected.
A two-class sampling scheme is defined by three numbers:
n – the number of sample units to be tested;
m – the count above which the sample is regarded as defective. This
term would not appear in schemes employing a presence/absence
test since a positive result is sufficient for the sample to be defective;
c – the maximum allowable number of sample units which may exceed
mbefore the lot is rejected.
Such schemes do not make full use of the numerical data obtained but
simply classify sample units according to the test result. For example, if
mis 10^4 cfu g^1 , those samples giving counts of 10^2 ,9 103 , and 1.2 104
would be considered acceptable, acceptable, and defective respectively,
despite the fact that the first sample had a count almost 2 log cycles lower
than the second and the difference in count between the second and third
samples is relatively small.
Using this approach, results from a number of sample units can be
classified according to the proportion defective and the frequency of
occurrence of defective units described by a binomial distribution. Ifp
represents the proportion of defective sample units in the whole lot,i.e.
the probability of a single sample unit being defective, andqrepresents
the proportion of acceptable units (the probability of a sample unit being
Chapter 11 399