**Question**

I like to know how to sample a finished product or ingredient so that the sample to be tested is representative of the product as a whole so it will increase confidence in subsequent test result. This is needed to verify a particular finished product lot or incoming ingredient lot is allergen free.

**Response**

Sampling is not a simple process of looking up a sample size in a table. There are many factors that influence how you develop a sampling plan. When I develop a QA program, I always try to develop the program to answer a specific question or develop a null hypothesis. Once I have framed the question, I can then develop a sampling plan to help develop the answer.

It appears that the question you would like to ask is the following:

• Is an allergen present in either a lot of finished product or in a lot of ingredient?

This question deals with an attribute issue.

In developing a plan, one needs to take into account a number of statistical assumptions including the following:

• Is the process relatively stable? In statistical process control terms, the process is rarely affected by special or assignable causes of variation. The following is an alternative way to describe a stable process. Is the allergen evenly distributed in the lot or can the allergen be concentrated in one part of the lot? Answering this question helps defines the unit.

• A random sampling plan must be used to select the units to be tested.

• A unit must be defined. The unit must either possess the characteristic or not possess the characteristic. The presence of the characteristic makes the unit defective. Many times in food sampling, a unit may be difficult to define.

• A test must be available that can determine if the unit contains the characteristic. It is permissible to test a portion of the unit as long as long as that portion of the unit correctly identifies whether the unit is or is not defective.

• A sampling plan must be developed in which the units will be collected. Every unit must have an equal chance of being selected for analysis (random sampling).

• The number of units that possess the characteristic must be small (less than 10%) as compared to the number of units that do not possess the characteristic. The removal of the number of units for analysis cannot affect the portion of defective units in the lot.

• The number of “units” in the lot does NOT affect the sensitivity of the attribute sampling plan.

• The portion of units that are defective is critical to the sampling plan. If the portion of defective units declines there needs to be an increase in the number of units sampled to ensure that the sensitivity or power of the sampling plan does not change.

• The total number of units sampled is critical for the sensitivity or power of the sampling plan. The power increases with an increase in number of units sampled and tested to determine if they are defective.

• If the portion of defective units can be estimated, it is possible to calculate the power of the sampling plan using the binomial distribution. Likewise, if a sampling plan is selected, it is possible to calculate the power of the sampling plan for a specific proportion of defective units.

• Need to define the confidence level that is desired to determine whether a lot contains or does not contain the allergen.

• Acceptance number. The smaller the acceptance number, the less of a risk the lot will contain units that are defective. The smaller the acceptance number the more sensitive the sampling plan.

The alternative method is to develop a QA system based on the concepts of process control. A classical approach is to use HACCP.

John G. Surak, PhD

– Providing food safety and quality solutions –

For more information on this topic, please visit ASQ’s website.