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OCR for page 132
6
Consideration of Sampling
Associated With a Criterion
An effective sampling plan is one of the essential components of a
microbiological criterion. The purpose of this chapter is to discuss the
most common sampling plans applicable to microbiological criteria for
foods. For more detailed information regarding statistical concepts of
population probabilities and sampling, choice of sampling procedures,
decision criteria, and practical aspects of application, the reader is referred
to publications such as those by the ICMSF (19741; Kilsby (19821; Kilsby
and Baird-Parker (19831; Kramer and Twigg (19701; Purl et al. (1979~;
and Purl and Mullen (19801. The ICMSF publication is especially useful
because it deals with statistically based sampling plans as applied to mi-
croorganisms in foods.
It is important to establish a sampling plan that can effectively discrim-
inate between good and bad lots. A lot in this case is defined as the
quantity of goods that has been produced, handled, and stored within a
limited period of time under uniform conditions. For example, the same
goods produced on a single line or processed in a day or during one shift
can be considered a lot. A lot is made up of sample units whose micro-
biological quality can be assessed. Sampling procedures and decision
criteria should be based on sound statistical concepts in order to achieve
a high degree of confidence in decisions relative to the acceptability of a
lot. A company may at times rely on a sampling plan in which the ex-
perience of its quality control personnel is used to select the location of
sampling, the number of sample units withdrawn from the lot, and the
limitts) for acceptance or rejection. Such procedures are often used in
investigations of rejected lots. Validity of the conclusion reached depends
on the ability of personnel to choose a representative sample. Only with
132
OCR for page 133
CONSIDERATION OF SAMPLING
133
a well-defined probability sample is the investigator guaranteed that the
sampling plan used has the stated properties, i.e., that it rejects inferior
batches with the stated frequency.
Many reviews regarding microbiological criteria deal with the problems
of sampling and decision criteria and recognize that reliable microbiol-
ogical criteria are not possible without a carefully chosen sampling plan
(Bartrum and Slocum, 1964; Charles, 1979; Corlett, 1974; Dyett, 1970;
Hobbs and Gilbert, 1970; Leininger et al., 1971; Shuffman and Kronick,
19631. Useful historical data on sampling and rejection criteria have re-
sulted from such studies. Factors to be considered in choosing a sampling
plan, as outlined by Kramer and Twigg (1970) include:
· purpose of inspection
· nature of product
· nature of the sampling and analytical procedure
· nature of the lots being examined
A common purpose of inspection and analysis of food, including mi-
crobiological testing, is to obtain information upon which to base a de-
cision to either accept or reject the food. The acceptability of a lot is
determined by selecting a suitable property or attribute, in this context,
whether or not some particular organism or group of organisms occurs in
number above a specified level.
The type of plan chosen for this purpose is termed an acceptance sam-
pling plan. The product type, its microbiological history, and its intended
use will influence the selection of the sampling plan. Difficulties in the
application of acceptance sampling plans that test for microbial levels in
foods have been outlined by a number of sources (Clark, 1978; Cowell
and Morisetti, 1969; Ingram and Kitchell, 1970; Kilsby et al., 1979;
Wodicka, 19734. The first difficulty arises in sampling because the mi-
croorganisms in many foods are often unevenly distributed within a lot,
e.g., Salmonella in dried milk powder. A second difficulty is related to
the errors inherent in the methods used to detect and enumerate micro-
organisms. (See Chapters 4 and 5.)
The International Commission on Microbiological Specifications for
Foods (ICMSF, 1974) has recognized many of these considerations by
relating the stringency of the sampling plan to the degree and type of
hazard of the food (Table 6- 1~. The stringency of sampling increases with
the hazard, from a condition of no health hazard but only of utility (shelf-
life) through a low indirect health hazard to direct health hazards related
to diseases of moderate or severe implication. For example, foods in the
"case 1" category present no direct health hazard. By contrast, foods in
the "case 15" category present a severe, direct health hazard where con
OCR for page 134
134 EVALUATION OF TlIE ROLE OF MICROBIOLOGICAL CRITERIA
ditions of handling and use after sampling may increase the hazard. Clin-
ical severity of a foodborne disease, available epidemiological information,
processing conditions, handling and ultimate use of the food are built into
these "case" numbers. A similar approach for selection of sampling plans
was adopted by the Committee on Evaluation of the Salmonella Problem
(NRC, 19691. The sampling plans proposed by this committee were rec-
ommended not for routine use but for application where a Salmonella
problem had been defined.
2-CLASS ATTRIBUTES SAMPLING PLANS
The 2-class attributes sampling plan simply classifies each sample unit
as acceptable (nondefective) or unacceptable (defective). In some plans,
the presence of any organism of a particular type, e.g., Salmonella, would
be unacceptable; in others, a limited number of organisms may ~ ac-
ceptable, e.g., Vibrio parahaemolyticus. In the latter, a boundary is
chosen, denoted by m, which divides an acceptable count from an un-
acceptable count. The 2-class plan rejects a lot if more than "c" out of
the "n" sample units tested were unacceptable.) For example, a typical
2-class plan with n = 5 and c = Q requires that five sample units be
tested and specifies a c value of 0 (see Table 6-1, case 101. The lot would
be rejected if any one of the five sample units tested was defective. Such
plans are used for Salmonella. The choice of n and c varies with the desired
stringency of the plan. By appropriate calculations the probability of ac-
ceptance can be determined for a lot of a given quality for any specified
sampling plan (see section below on operating characteristic curves). These
sampling plans are valid regardless of the statistical distributions of the
microbiological counts provided that an appropriate probability sampling
scheme has been used to select the units to be tested.
Military Standard 105D (DOD, 1963), which was developed to meet
mass-production quality requirements during World War II, is a prime
example of statistically designed single and multiple 2-class attributes
in = number of sample units analyzed which are chosen separately and independently.
c = maximum allowable number of sample units yielding unsatisfactory test results, e.g.,
the presence of the organism, or a count above m.
m = a microbiological criterion that in a 2-class plan separates good quality from defective
quality; or in a 3-class plan separates good quality from marginally acceptable quality.
M = a microbiological criterion that in a 3-class plan separates marginally acceptable quality
from defective quality. Values at or above M are unacceptable.
case = a set of circumstances related to the nature and treatment of a food, categorized into
15 such sets which influence the anticipated hazard from the presence of specified bacterial
species or groups within a food (ICMSF, 1974).
OCR for page 135
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OCR for page 136
136 EVALUATION OF THE ROLE OF MICROBIOLOGICAL CRITERIA
sampling plans. These concepts were used also in sampling plans for
Salmonella by the committee evaluating the Salmonella problem (NRC,
1969).
3-CLASS ATTRIBUTES SAMPLING PLANS
Because the choice of a boundary between an acceptable count and an
unacceptable count is rather arbitrary, Bray et al. (1973) introduced the
concept of a 3-class plan. Sample units with a count of less than m are
of acceptable or good quality. Units with a count between m and M (see
footnote 1) are judged to be of marginal quality, and units whose counts
are greater than M are of unacceptable or bad quality. A random sample
of n sample units would be chosen from the lot and the lot would be
rejected if any of the sample units had a count above M and/or if more
than c of the units had a count above m. For example, a typical 3-class
plan is characterized by n = 5, c = 2, m = 105/g, M = 107/g. Thus
five sample units (n = 5) are analyzed. The lot will be rejected if any
sample unit exceeds a count of 107/g and/or if three or more sample units
exceed a count of lOs/g. The lot will be accepted if all units have counts
of less than 107/g and if no more than two units have counts greater than
lOs/g.
The 3-class plan makes no assumption about the distribution of counts
in the lot. It assumes only that an appropriate probability sampling pro-
cedure was used to select the sample units. As with 2-class plans, the
choice of n and c varies with the desired stringency of the plan. The
ICMSF (1974) has applied 2- and 3-class attributes sampling plans to
assess microbiological safety or quality for a variety of foods involved in
international trade.
VARIABLES SAMPLING PLANS
As stated previously, for the 2-class attributes sampling plan, no as-
sumption is necessary regarding the distribution of counts in the population
of sample units from which the sample is taken. When the distribution of
counts is known, this additional information can be used to increase the
chance of making a correct decision or equivalently to reduce the sample
size while maintaining the same probability of a correct decision.
Frequently it is assumed that the log of the count follows a normal
distribution. Kilsby and coworkers (Kilsby, 1982; Kilsby and Pugh, 1981;
Kilsby et al., 1979) have stated that this assumption is reasonable when
the food comes from a common source and is processed under uniform
conditions. The variables plan is chosen so as to reject a lot with probability
OCR for page 137
CONSIDERATION OF SAMPLING
137
P if the proportion of unacceptable sample units (as defined in the 2-class
attributes plan) exceeds p (a proportion). For example, if more than 10%
of the sample units are unacceptable, the goal is to reject the lot with 80%
probability. The rule for deciding whether to reject a lot is the following:
reject the lot if x + ks ~ m where x and s are the sample mean and
standard deviation of the log counts from a sample of size n. The value
m is some microbiological concentration that is critical. The value k is
determined from the noncentral t-distribution (Johnson and Welch, 19401.
OPERATING CHARACTERISTIC CURVES
In general, it is necessary to balance the probabilities of two risks in
acceptance sampling. The acceptance quality level is defined as the max-
imum proportion of unacceptable sample units that a lot can possess and
still be acceptable. Some larger proportion of defective units, judged to
be the minimum proportion of defective units for which the lot is entirely
unacceptable might be termed the defective quality level. For example, a
lot with fewer than 5% defective units might be judged entirely acceptable
but with more than 10% defective units might be judged entirely unac-
ceptable. The zone between 5% and 10% defective units might be termed
a zone of indifference. The acceptable quality level is 5% and the defective
quality level is 10%. The vendors' or producers' risk is the probability
that a lot of acceptable quality level is rejected. The consumers' or buyers'
risk is the probability that a lot of defective quality level is accepted. The
operating characteristic (OC) curve provides the information necessary to
evaluate these risks. For a 2-class attributes sampling plan, the OC curve
is simply the probability of accepting the lot, plotted as a function of the
true proportion of detectives in the lot.
Figure 6-1 gives the OC curve for an attributes sampling plan in which
n = 10 and c = 2. The lot is rejected if more than two samples are found
to be defective. A lot with 20% defective sample units would be accepted
68% of the time and rejected 32% of the time. With 40% defective units,
the lot would be accepted 17% of the time, and with only 10% defective
units, the lot would be accepted 93% of the time. With this information,
it is possible to judge whether both the consumers' and the producers'
interests are being met.
The influence of the c value on the OC curve can be seen in Figure
6-2. Increasing c but holding n at a fixed value causes a lot with a larger
proportion of defective units to be accepted. Increasing n but holding the
c/n constant (i.e., the maximum proportion of detectives tolerated) causes
the OC curve to become steeper (Figure 6-31. This means that the ability
to discriminate between acceptable and unacceptable lots has been in
OCR for page 138
138 EVALUATION OF THE ROLE OF MlCROBlOLOGICAL CRITERIA
creased. For example, with a sample size of n = 5 and c = 1, there is
a 0.20 probability of rejecting a lot with 17% defective units and a 0.20
probability of accepting a lot with 49% defective units. With a sample
size of n = 10 and c = 2, there is a 0.20 probability of rejecting a lot
with 16% defective units and a 0.20 probability of accepting a lot with
38% defective units. For n = 20 and c = 4, these percentages become
16 and 29.6, respectively. It is apparent from these examples that as the
sample size increases, the difference between producers' and consumers'
risks can be made smaller. In fact, one can calculate the minimum sample
size required to satisfy prescribed producers' and consumers' risks. A1-
ternatively, if the sample size and one of the risks is specified, the other
risk is determined and can be calculated.
1 .00
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p = Percent of Defective Sample Units Comprising Lot
1.00
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FIGURE 6-1 The operating characteristic curve for n = 10, c = 2, i.e., the prob-
ahilitv of accenting lots. in relation to the proportion defective among the sample units
eve ~ a- ___-r -~''D '~ A ~ ~~~ ~ ~~~~~~~~ A r - - ~
comprising the lots.
SOURCE: ICMSF, 1974, p. 7. Copyright A) 1974 by University of Toronto Press.
OCR for page 139
CONSIDERATION OF SAMPLING
1 .00
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PERCENT DEFECTIVE (Pd)
139
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PERCENT DEFECTIVE (Pd)
n= 20
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~ `141
0 20 40 60 80
PERCENT DEFECTIVE (Pd)
FIGURE 6-2 Operating characteristic curves for different sample sizes (n) and dif-
ferent criteria of acceptance (c) for 2-class attributes plan.
SOURCE: ICMSF, 1974, p. 24. Copyright ~ 1974 by University of Toronto Press.
It is important to note that unless the proportion of the lot sampled is
greater than 10%, the size of the lot has very little effect on the probability
of acceptance. In fact, OC curves for attributes plans are normally com-
puted assuming an infinite lot size and using the binomial distribution.
When the sample size exceeds 10% of the lot size, the binomial distribution
should be replaced by the hypergeometric distribution for computing prob-
abilities of acceptance (Purl and Mullen, 1980~.
In the 3-class plans the OC curve is replaced by an OC surface. For
these plans the probability of accepting the lot is plotted as a function of
the proportion of defective or unacceptable sample units and the proportion
OCR for page 140
140 EVALUATION OF THE ROLE OF MICROBIOLOGICAL CRITERIA
o
1.00
~ 0.80-
z
~ 0.60
11
° 0.40
~ 0.20
CD
o
0.00
\\\n= 10
\~20
0 20 40 60 80
PERCENT OF DEFECTIVE SAMPLE UNITS
FIGURE 6-3 Operating characteristic curves for different sample sizes n keeping
*c/n constant for two-class attributes plan (*c = criteria for acceptance).
Of marginally acceptable sample units. The ICMSF (1974) publication
contains tables giving the probability of acceptance for various proportions
of defective and marginally acceptable sample units for commonly used
3-class attributes plans.
Sampling plans for use in the microbiological examination of foods are
usually by necessity single sampling plans based on one sample size with
a number of sample units, because the analytical procedures are frequently
destructive and time-consuming. Such conditions generally make double
or sequential sampling plans uneconomical for frequent application in
microbiological criteria. Sequential sampling plans are used, however, in
visual nondestructive examination of canned foods for physical defects
such as dents or overall seam measurement.
ESTABLISHING LIMITS
Limits expressed in sampling plans can be determined in two ways.
One method is to use data generated by surveys. When using appropriate
probability sampling techniques, results from surveys can produce un-
biased estimates of the mean and standard deviation of the distribution of
the desired microbiological parameter (Purl and Mullen, 1980; Sukhatme
OCR for page 141
CONSIDERATION OF SAMPLING
141
and Sukhatme, 1970). It may be appropriate to first transform the scale
of measurement of the desired parameter. For example, frequently the
logs of the microbiological counts follow a normal distribution more closely
than the counts themselves. Collins-Thompson et al. (1978) chose m to
be x + 2s where x and s are the sample mean and sample standard
deviation based on a national survey. If the microbiological parameters
under consideration follow a normal distribution, then approximately 2.5%
of the sample units would exceed m. Hence this approach implicitly
assumes that at the time of the survey only 2.5% of sample units are
unacceptable.
Corlett (1974) described the process of determining limits by judging
count levels consistent with Good Manufacturing Practices (GMP). For
example, if a product consistently yielded counts of less than, say, 10
coliforms per gram under good processing controls, then this level would
be used as a limit. This approach to selection of limits appears to be
common and practical. A further approach to judgment limits was sigh
gested by Davis (19691. Since there are inherent errors in microbiological
testing, he proposed a 3-tier system of limits that differs by multiples of
10. Using his example, raw meat for pies would be declared satisfactory
(S) when total counts were under 106/g, doubtful (D) when counts ranged
between 106 and 107/g and unsatisfactory (U) when counts exceeded 107/
g. This SDU system is somewhat analogous to the 3-class ICMSF sampling
plan (ICMSF, 1974) where a m value represents levels consistent with
GMP and the M value is the smallest value that poses a health hazard,
spoilage, or an overt sanitation problem. The M value should not be used
to reflect GMP nor should it be set at some arbitrary level, for example,
where 98% of the lots can meet it. This is a misuse of the philosophy
behind the establishment of this value. The M value should be chosen
based on expert judgment and historical data. The establishment of limits
for variables sampling plans for commodities such as meat has been de-
scribed by Kilsby (1982) and Brown and Baird-Parker (19821.
RESAMPLING
No discussion about sampling plans is complete without discussing the
problem of resampling. This problem, described by Pitt (1978) as the
resampling syndrome, is a common practice when the first set of analyses
yields unfavorable results. By resampling, we mean that when the initial
sample yields results that are unacceptable, a second sample may be taken.
If the test results on this sample are favorable, the lot is then accepted.
(Pitt t1978] further associates this situation to ancient times when mes-
sengers who brought bad news were killed or made to repeat the journey
OCR for page 142
142 EVALUATION OF THE ROLE OF MICROBIOLOGICAL CRITERIA
until glad tidings were delivered.) Resampling changes the characteristics
of the sampling plan, for example, by increasing the probability of ac-
cepting lots of poor quality. This becomes a problem if the investigator
believes that the operating characteristic curve associated with the original
1-sta~e sampling clan is still valid. It is not! For example, in sampling a
,, 1 it,, ~ , , _
lot with 20~o defective units, a 2-class attributes sampling plan (n = a,
c = 0) will accept the lot only 33% of the time. If resampling is allowed
when one unacceptable unit is detected and the lot is accepted if no further
unacceptable units occur in the next five units sampled, then the probability
of accepting the lot increases to 46%. Decision criteria based upon an
undetermined OC curve can lead to incorrect decisions about the accept-
ability of the lot. This situation is aggravated because resampling is un-
dertaken only on selective occasions when lots have been rejected. (For
additional information see Appendix A-I and ICMSF, 1974, p. 71~.
This is not to say that resampling is always wrong since there are
occasions when testing for pathogens such as Salmonella may produce a
false-positive result and retesting is necessary. The Salmonella committee
offered a corresponding solution to this problem (NRC, 1969) when it
proposed a 2-stage sampling plan to avoid rejection on the basis of a single
positive test. Thus, the acceptance criteria for a lot are based on a 2-stage
sampling plan with determined probabilities. Two-stage sampling plans,
when properly used, can reduce the average sample size necessary to
achieve adequate protection because, with badly contaminated lots, a small
first-stage sample may be sufficient to reject the lot. A second-stage sample
is then needed only for doubtful cases.
When resampling is required the consequences of this procedure should
be included in the final decision criterion. Resampling is useful during
investigational proceedings. When it is established that a lot is unaccept-
able, one may wish to reexamine it to determine selective salvage or
corrective measures (see Chapter 71. This increase in data generated by
resampling can prove to be beneficial in reaching sensible and realistic
. .
c .eclslons.
APPLICATIONS
There are two prime reasons for microbiological sampling. The first is
to enable a decision to be reached on the suitability of a food or ingredient
for its intended purpose. The ICMSF 2- and 3-class attributes sampling
plans are appropriate for this purpose. These plans are used in Canada on
a national basis and are incorporated in legislative programs (see Chapter 81.
The second reason for microbiological sampling is to monitor performance
relative to accepted Good Manufacturing Practices. Attributes sampling
OCR for page 143
CONSIDERATION OF SAMPLING
143
may also be applicable when sample units can be appropriately drawn at
critical control points (including end product). On the other hand, sampling
may be required to detect faulty cleaning or some other neglectful practice
by, for example, analyzing for "indicator organisms." It is also likely
that samples would be taken at critical control points to detect an unusual
change in the extent of contamination or growth.
In many instances, including the preceding examples, attributes sam-
pling may not be applicable because there may be no defined lot and
random sampling may not be possible. Nevertheless, the analytical results
may be used by experienced personnel to assess the performance of the
critical control point.
There are other statistically based systems by which analytical results
can be assessed as to validity in reaching a decision, e.g., variables
sampling (Kilsby and Baird-Parker, 19831. Additional studies are needed
to determine the extent to which these systems are suitable for foods.
REFERENCES
Bartram, M. T., and G. G. Slocum
1964 Microbiological criteria for foods. IV. Problems of sampling and interpretation of
bacteriological results on frozen foods. J. Assoc. Food Drug Off. of the U.S. Quart.
Bull. 30(1):14-17.
Bray, D. F., D. A. Lyon, and I. Burr
1973 Three-class attributes plans in acceptance sampling. Technometrics 15:575.
Brown, M. H., and A. C. Baird-Parker
1982 The microbiological examination of meat. In Meat Microbiology. M. H. Brown, ed.
London: Applied Science. Pp. 423-509.
Charles, R.H.G.
1979 Microbiological standards for foodstuffs. Health Trends 11:1-4.
Clark, D. S.
1978 The International Commission on Microbiological Specifications for Foods. Food
Technol. 32(1):51-54, 67.
Collins-Thompson, D. L., K. F. Weiss, G. W. Riedel, and S. Charbonneau
1978 Sampling plans and guidelines for domestic and imported cocoa from a Canadian
national microbiological survey. Can. Inst. Food Sci. Technol. J. 11:177-179.
Corlett, D. A., Jr.
1974 Setting microbial limits in the food industry. Food Technol. 28(10):34-40.
Cowell, N. D., and M. D. Morisetti
1969 Microbiological techniques some statistical aspects. J. Sci. Food Agric. 20:573-
579.
Davis, J. G.
1969 Microbiological standards for foods. Part 2. Lab. Practice 18:839-845.
DOD (U.S. Department of Defense)
1963 Military Standard 105D. Sampling procedures and tables for inspection by attributes.
Washington, D.C.: DOD.
Dyett, E. J.
1970 Microbiological standards applicable in the food factory. Chem. and Ind. 189-192.
OCR for page 144
144 EVALUATION OF THE ROLE OF MICROBIOLOGICAL CRITERIA
Hobbs, B. C., and R. J. Gilbert
1970 Microbiological standards for food: public health aspects. Chem. and Ind. 215-219.
ICMSF (International Commission on Microbiological Specifications for Foods)
1974 Microorganisms in Foods. 2. Sampling for microbiological analysis: Principles and
specific applications. Toronto: University of Toronto Press.
Ingram, M., and A. G. Kitchell
1970 Symposium on microbiological standards for foods. Chem. and Ind. 186-188.
Johnson, N. L., and B. L. Welch
1940 Applications of the non-central t-distribution. Biometrika 31:362-389.
Kilsby, D. C.
1982 Sampling schemes and limits. In Meat Microbiology. M. H. Brown, ed. London:
Applied Science. Pp. 387-421.
Kilsby, D. C., and A. C. Baird-Parker
1983 Sampling programs for the microbiological analysis of foods. In Food Microbiology:
Advances and Prospects. T. A. Roberts and F. A. Skinner, eds. London and New
York: Academic Press.
Kilsby, D. C., and M. E. Pugh
1981 The relevance of the distribution of microorganisms within batches of food to the
control of microbiological hazards from food. J. Appl. Bacteriol. 51:345-354.
Kilsby, D. C., L. J. Aspinall, and A. C. Baird-Parker
1979 A system for setting numerical microbiological specifications for foods. J. Appl.
Bacteriol. 46:591-599.
Kramer, A., and B. A. Twigg
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58.
Representative terms from entire chapter:
sampling plans
