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Acceptance sampling
Definition
Acceptance sampling is a procedure for deciding what to do with a lot or batch by inspecting a sample rather than every item. A predefined sampling plan specifies how items are selected, what is measured and which results lead to acceptance, rejection or further sampling. Its primary purpose is a lot-disposition decision.
What it means
The procedure trades inspection effort against the risk of a wrong decision. A good lot can be rejected because an unlucky sample contains too many nonconforming items, while a poor lot can be accepted because its sample happens to look satisfactory.
Acceptance sampling is therefore different from proving that every item is conforming. It is also different from estimating a defect rate with a chosen precision, although the same inspection data may contain information about quality. A plan designed for a disposition decision should not automatically be assumed adequate for a separate estimation objective.
How it works
Start by defining the lot, the inspection characteristic and the decision consequences. Select an appropriate plan before observing the sample. In a single-sample attributes plan, draw n items using the specified random selection procedure, count nonconforming units and accept if that count is at most c.
Other plans use two or more stages, allowing a decision after an early sample or requiring additional evidence. Variables plans use measured quantities under their own assumptions instead of only a conforming/nonconforming count.
The operating-characteristic curve describes acceptance probability across possible quality levels. Plan design considers protection for both producer and consumer, along with inspection cost and any applicable scheme. Representative sampling and reliable inspection are essential: a carefully calculated plan cannot compensate for taking only the easiest items to reach or misclassifying their condition.
Three practical examples
1. A manufacturer samples a delivery of components when inspecting every unit would be expensive, using a specified acceptance rule and supplier agreement.
2. A packaging company uses a plan for a destructive strength test, since testing every package would leave none available for use.
3. A records-processing team inspects randomly selected entries from a completed batch and uses predefined error criteria to decide whether that batch requires rework.
Think of it this way
Think of checking a batch through a carefully chosen window. The window gives evidence about the batch, but it does not reveal every item. The sampling plan specifies how large that window is and what observations trigger a decision, while acknowledging that some uncertainty remains outside it.
Worked example
Consider an original illustrative single-sample plan: inspect 20 randomly selected units and accept the lot if no more than one is nonconforming. A sample containing zero or one nonconforming unit passes; a sample containing two fails. This is a teaching example, not a recommended production plan.
Assume a large lot and a binomial approximation with nonconforming probability p = 0.05. The probability of acceptance is P(X=0)+P(X=1) = 0.95^20 + 20(0.05)(0.95^19), approximately 0.73584. The probability of rejection is approximately 0.26416.
Thus, repeated lots with the same underlying 5% nonconforming proportion can receive different decisions because their random samples differ. If sampling without replacement from a small finite lot with a fixed number of nonconforming units, the exact count model is hypergeometric rather than binomial. The sampling assumptions belong with the reported probability.
Illustrative case study
Fictional case study: BatchBridge checks scanned records before importing them into an archive. Its initial routine samples the first twenty records, which are usually produced by the most experienced operator.
The team replaces that convenience selection with a documented random sample across the defined batch. It also clarifies whether multiple errors within one record count as one nonconforming record or several nonconformities. Rejected batches follow a stated rework process, rather than being repeatedly resampled until one sample passes.
This fictional case illustrates how selection and definitions affect a sampling procedure. It does not establish that twenty records are enough for the intended risks or claim that a passing batch is free of errors.
Common misconceptions and mistakes
Acceptance is not a certificate that every item is good, and rejection does not mean every item is bad. Another mistake is choosing or relaxing the acceptance threshold after seeing the sample. That changes the plan's operating characteristics.
Do not repeatedly take fresh samples until a lot passes unless the specified procedure explicitly accounts for that process. A zero-defect sample also does not establish a zero-defect lot. Finally, a sampling plan does not remove the need to understand production causes: inspection decisions and process improvement address different questions.
Business use
Acceptance sampling can make inspection effort predictable and lot decisions more consistent. It is useful when full inspection is costly, slow or destructive, provided the remaining risks are appropriate for the application.
Document the lot boundaries, sampling frame, randomization, inspection method and response to each decision. Track the actual outcomes and review whether suppliers or processes change over time. Where a continuing-lot scheme uses switching rules, apply the scheme as a whole rather than extracting one convenient sample size. Decide separately whether additional investigation or corrective action is needed after repeated quality problems.
People also ask
Is acceptance sampling the same as statistical process control?
No. Acceptance sampling concerns disposition of lots, while process control monitors process behavior over time. They can complement one another.
Does a larger sample always solve the problem?
More information can improve discrimination when the plan is designed appropriately, but biased selection or inaccurate inspection can still undermine the decision.
What is the acceptance number?
In a simple attributes plan, it is the largest allowed count of nonconforming units in the sample for accepting the lot. It is not the lot's true defect percentage.
Check your understanding
A predefined plan has sample size 30 and acceptance number two. The inspector finds three nonconforming units. May the lot be accepted because most sampled units were good?
Answer: No. Under that rule, three exceeds two, so the lot is rejected. Any alternative disposition must follow the agreed procedure rather than an improvised reinterpretation.
Related terms
- acceptance quality limit
- acceptance number
- producer's risk
- consumer's risk
- operating-characteristic curve
- attributes inspection
- variables sampling
- binomial distribution and hypergeometric distribution
Learn next
calculate and plot acceptance probabilities for several underlying defect levels under one simple plan. Then compare a second plan with different sample size and acceptance number. Explain the inspection burden and risks rather than judging the plans by sample size alone.
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Sources
Primary sources: NIST/SEMATECH, What is Acceptance Sampling?: https://www.itl.nist.gov/div898/handbook/pmc/section2/pmc21.htm
NIST/SEMATECH, Lot Acceptance Sampling Plans: https://www.itl.nist.gov/div898/handbook/pmc/section2/pmc22.htm
NIST/SEMATECH, Choosing a Sampling Plan with a given OC Curve: https://www.itl.nist.gov/div898/handbook/pmc/section2/pmc222.htm
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