SOP: Acceptance Sampling of Lots by Attributes — Single Sampling

GIFSQ — Global Institute for Food Safety & Quality

Principle

Inspection by attributes judges each unit only as acceptable or unacceptable — good or bad. It suits two kinds of characteristics: those that cannot be measured (scratches, damage), and those that could be measured but are not, because of time, cost or need. Inspection by variables is the contrast: it records actual measured values, for example °Brix and juice yield of oranges, the basis on which payment is made in orange-juice concentrate plants.

Quality characteristics fall into three classes: critical (a health hazard to the consumer — microbial contamination, toxic substances), major (determine the ultimate quality of the product — Brix-acid ratio in citrus fruits, alcohol-insoluble solids in peas and corn, tomato colour), and minor (a defect that can be sorted out or removed in preparatory processes).

The Acceptable Quality Level (AQL) is the maximum number of defects per 100 units that may be considered satisfactory as a process average for sampling inspection; the producer’s risk α is nominally 0.05 (in practice 0.01 to 0.10). The attribute plan (MIL-STD 105D, adopted as ISO/DIS 2859) applies to raw materials, operations, materials in process, products and supplies in storage. It provides three general inspection levels: II (normal use), I (about half the inspection) and III (about twice the inspection, a steeper operating-characteristic curve, more discrimination and higher inspection cost). Special levels S-1 to S-4 use small sample sizes where large sampling risks can or must be tolerated.

A single sampling plan is defined by N (lot size), n (sample size), and the acceptance number Ac with its rejection number Re.

Procedure

From the lot size and the inspection level, find the sample-size code letter in the code-letter table

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From the code letter and the AQL, find n, Ac and Re in the single-sampling table for normal inspection

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Draw a random sample of n units from the lot — every unit gets an equal likelihood of selection

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Count the defective units in the sample

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Accept the lot if the defective count is at or below Ac; reject the lot if it reaches Re

Worked example: a truck-load of about 18,000 mature mangoes; factory specification limits spoiled or damaged fruit to 1%. Lot size N = 18,000 at inspection level II gives code letter M from the code-letter table. At AQL 1.0%, code M gives n = 315, Ac = 7, Re = 8. Inspect a random 315 fruits: 7 or fewer spoiled means the load is accepted; 8 or more spoiled means it is rejected. Tightened inspection calls for code letter N: n = 500, Ac = 10, Re = 11. Reduced inspection calls for code letter K: n = 125, Ac = 3, Re = 4.

Note: the scanned single, double and multiple sampling tables are garbled and are not reproduced here; use the printed MIL-STD 105D tables — normal inspection in the single-sampling table, with the tightened and reduced tables in the printed MIL-STD 105D standard — to look up n, Ac and Re for the code letter and AQL found above. The tightened table in the extraction prints the rejection number as “11.0n”; carried here as 11.

Arrow rule: where acceptance and rejection numbers are missing from a table section, arrows appear instead. A downward arrow means the adjacent sample size is too small — use the next lower section of the table (for example, lot size 50 at level II gives code D, but at AQL 1.0% a downward arrow points to the code-E section, n = 13, Ac = 0, Re = 1). An upward arrow means use the preceding smaller section (for example, code R at AQL 10% points upward to the code-Q section).

Precautions

• Random sampling is essential — the whole plan rests on every piece in the lot having an equal likelihood of being selected.
• Sample size depends on the homogeneity of the material, the size of the unit, the reliability of the source, the cost of the material, the importance of the test, whether the test is destructive, the time the test takes, and its cost.
• Tighten inspection (more samples) when risk must be minimized; reduce it only when the buyer is confident of the source and prepared to take the normal risk.

References

Ranganna, S., Handbook of Analysis and Quality Control for Fruit and Vegetable Products, 2nd edition.

MIL-STD 105D attribute sampling (ISO/DIS 2859) — cited in the book.