SOP: Using the Operating Characteristic Curve of a Sampling Plan

GIFSQ — Global Institute for Food Safety & Quality

Principle

Every sampling plan can be fully described by its operating characteristic (OC) curve — probability of acceptance plotted against the per-cent defective in the lot. The curve shows both the producer’s and the consumer’s risk, and the steeper the curve, the better the plan discriminates between good and bad lots (level III inspection gives a steeper curve than level II for this reason).

Procedure

Find the lot’s per-cent defective on the bottom axis of the OC curve for the code letter and AQL in use

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Follow the vertical line up from that point until it reaches the curve

↓

At that level, read the acceptance percentage on the left axis and the rejection percentage on the right axis

Worked example (single sampling plan, sample-size code letter N, AQL 1.0%): if the lot contains 3% spoiled fruits, the vertical line from 3% meets the curve at 87% on the rejection scale to the right — that is, about 13% acceptance, so roughly 13% of the time this plan will accept a lot with 3% spoiled fruit. If the lot contains only 1% spoiled fruits, the plan accepts it 98% of the time (probability 0.98).

Note: OC curves for different sample-size code letters may be constructed following any book on quality control.

Precautions

• Read the curve that belongs to the code letter and AQL actually in use — each plan has its own curve.
• Use the curve’s discrimination (its steepness) to judge whether the plan fits the purpose; a flatter curve accepts poor lots more often.

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.