Question
I am plant production specialist working in government sector. I am the manager of pesticides residues surveillance program, on this program we targeting local commodities of fresh fruits and vegetables (F&V) by sampling the targeted numbers and types of F&V in regular basis around the year and we analyze samples and results and establish the annual report. I have checked many similar program in other countries included USDA program but I didn’t find approach methodology or statistical way to identify the sample size to be targeted in the year taking in account type and number of crops, crop production,…etc. to elaborate annual sampling plan. My question here is how can elaborate sampling plan for mentioned program considering all valuable factors?
Your cooperation is highly appreciated.
Answer
Sampling is a method to estimate population parameters. For example, if the goal is to determine the amount of unacceptable residue on store bought apples, and testing every individual apple is impractical, then we use a sample to estimate the proportion with unacceptable residue.
The sample plan must focus on the goal and balance with the resources and technology available. If the goal is to accurately detect a very low proportion with residue, say 1 in 1 million, then the sample size will be larger than if the goal is to detect 1 in 100 with unacceptable residue. The goal to detect 1 in 100 is easier to accomplish (fewer apples tested) yet does not reveal is there is a 1 in 1000 level or not.
A key element is the specific goal for detection and design a sample plan that is capable to detect at or better than the goal’s level. Capable includes the measurement system errors and an understanding of the nature of how failures occur.
Another consideration is the nature of the measurement and goal. If the test is only pass / fail for presence of residue, then we have to use the relatively inefficient sampling plans based on the binomial distribution. If the data is a variable value, such as part per million residue presence, then we can use more efficient sampling plans based on the appropriate continuous distribution. If the testing is destructive to the item being tested that limits the sampling techniques available.
How is the lot defined? If this is an annual report then the lot may be the annual production of a specific fruit or vegetable, say a specific variety of apples. Define the population clearly and any relevant subgroups of interest. If the data is only for an annual report the sampling plan is marked different than if the goal is a monthly monitoring and warning system.
Another consideration is the thresholds along with confidence. For sampling plan creation we use two specific points of interest. The Producer Risk Point (PRP) made up of the Acceptable Quality Level (AQL) and the producers’ risk (Type I risk or Alpha – which is the probability of rejecting a good lot, or in this case stating the residual level is above a specific AQL or value when it actually is not). The second point is the Consumer’s Risk Point made up of the Lot Tolerance Percent Defective (LTPD) and the consumer’s risk (Type II risk or Beta – which is the probability of accepting a bad lot, or in this case stating the residual level is below the LTPD when it is actually is not.)
The closer the AQL and LTPD are the more difficult (more samples) it is to determine an accurate estimate of the population. Likewise the less risk either the producer or consumer desire to incur again results in higher sample sizes.
One more consideration which is often overlooked is the selection of samples for testing. Most sampling plans are based on the assumption that the samples are taken randomly from the entire population. For example with say 50 million apples of a specific variety we would create a system to select samples that each has an equal change of any specific apply being selected. This is not a trivial matter in most cases. The availability and distribution of apples along with storage, shipping and display of apples all contribute to limited or biasing selecting a random sample. If it is not possible to select test items randomly, then study the impact on the study and means to account for a non-random sample.
In summary, for any sample plan:
- Define the population
- Define the desire goal of the study
- Understand the measurement system
- Use variables data if at all possible
- Define PRP and CRP
- Determine capable sampling plan
- Design method to select random sample
This quick summary of consideration is what I consider the essential elements, yet other may impact the sampling plan. For example, seasonal variations in production, location in supply chain when measurements are made, variations in supply chain impact on presence of residual, differing nature of residue commonly found of different fruit or vegetables, and probably a few more. Understanding the goal, measurement system and random sampling will help determine areas that require consideration.
Cheers,
For more on this topic, please visit ASQ’s website.