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National Research Council (US) Subcommittee on Microbiological Criteria. An Evaluation of the Role of Microbiological Criteria for Foods and Food Ingredients. Washington (DC): National Academies Press (US); 1985.
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 (1974); Kilsby (1982); Kilsby and Baird-Parker (1983); Kramer and Twigg (1970); Puri et al. (1979); and Puri and Mullen (1980). The ICMSF publication is especially useful because it deals with statistically based sampling plans as applied to microorganisms in foods.
It is important to establish a sampling plant that can effectively discriminate 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 microbiological 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the experience of its quality control personnel is used to select the location of sampling, the number of sample units withdrawn from the lot, and the limit(s) for acceptance or rejection.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 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 microbiological 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, 1963). Useful historical data on sampling and rejection criteria have resulted 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 examinedA common purpose of inspection and analysis of food, including microbiological testing, is to obtain information upon which to base a decision 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 sampling 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, 1973). The first difficulty arises in sampling because the microorganisms 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 microorganisms. (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 (shelflife) 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 conditions of handling and use after sampling may increase the hazard. Clinical 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, 1969). The sampling plans proposed by this committee were recommended not for routine use but for application where a Salmonella problem had been defined.
Suggested Sampling Plans for Combinations of Degrees of Health Hazard and Conditions of Use (i.e., the 15 'Cases').
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 be acceptable, e.g., Vibrio parahaemolyticus. In the latter, a boundary is chosen, denoted by m, which divides an acceptable count from an unacceptable count. The 2-class plan rejects a lot if more than "c" out of the "n" sample units tested were unacceptable. 1 For example, a typical 2-class plan with n = 5 and c = 0 requires that five sample units be tested and specifies a c value of 0 (see Table 6-1, case 10). 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 acceptance 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 sampling plans. These concepts were used also in sampling plans for Salmonella by the committee evaluating the Salmonella problem (NRC, 1969).
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 = 10 5 /g, M = 10 7 /g. Thus five sample units (n = 5) are analyzed. The lot will be rejected if any sample unit exceeds a count of 10 7 /g and/or if three or more sample units exceed a count of 10 5 /g. The lot will be accepted if all units have counts of less than 10 7 /g and if no more than two units have counts greater than 10 5 /g.
The 3-class plan makes no assumption about the distribution of counts in the lot. It assumes only that an appropriate probability sampling procedure 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.
As stated previously, for the 2-class attributes sampling plan, no assumption 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 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 + ks > m where 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, 1940).
In general, it is necessary to balance the probabilities of two risks in acceptance sampling. The acceptance quality level is defined as the maximum 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 unacceptable. 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 (OCR) 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 defectives 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 operating characteristic curve for n = 10, c = 2, i.e., the probability of accepting lots, in relation to the proportion defective among the sample units comprising the lots. SOURCE: ICMSF, 1974, p. 7. Copyright © 1974 by University of Toronto (more. )
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 defectives tolerated) causes the OC curve to become steeper (Figure 6-3). This means that the ability to discriminate between acceptable and unacceptable lots has been increased.
Operating characteristic curves for different sample sizes (n) and different criteria of acceptance (c) for 2-class attributes plan. SOURCE: ICMSF, 1974, p. 24. Copyright © 1974 by University of Toronto Press.
Operating characteristic curves for different sample sizes n keeping *c/n constant for two-class attributes plan (*c = criteria for acceptance).
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. Alternatively, if the sample size and one of the risks is specified, the other risk is determined and can be calculated.
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 computed 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 probabilities of acceptance (Puri 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 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.
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 unbiased estimates of the mean and standard deviation of the distribution of the desired microbiological parameter (Puri and Mullen, 1980; Sukhatme 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 + 2s where 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 suggested by Davis (1969). 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 10 6 /g, doubtful (D) when counts ranged between 10 6 and 10 7 /g and unsatisfactory (U) when counts exceeded 10 7 /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 described by Kilsby (1982) and Brown and Baird-Parker (1982).
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 [1978] further associates this situation to ancient times when messengers who brought bad news were killed or made to repeat the journey until glad tidings were delivered.) Resampling changes the characteristics of the sampling plan, for example, by increasing the probability of accepting lots of poor quality. This becomes a problem if the investigator believes that the operating characteristic curve associated with the original 1-stage sampling plan is still valid. It is not! For example, in sampling a lot with 20% defective units, a 2-class attributes sampling plan (n = 5, 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 acceptability of the lot. This situation is aggravated because resampling is undertaken 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 unacceptable, one may wish to reexamine it to determine selective salvage or corrective measures (see Chapter 7). This increase in data generated by resampling can prove to be beneficial in reaching sensible and realistic decisions.
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 8). The second reason for microbiological sampling is to monitor performance relative to accepted Good Manufacturing Practices. Attributes sampling 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 sampling 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, 1983). Additional studies are needed to determine the extent to which these systems are suitable for foods.
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n = 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).
