Definition:Acceptance Sampling
Definition
Acceptance sampling is a procedure in quality control in which:
- $(1): \quad$ a sample is taken from a batch and measured
- $(2): \quad$ the number of defectives is counted
- $(3): \quad$ a decision is made to accept or reject the batch based on the number of those defectives.
Motivation
Every batch of items of merchandise may contain defectives.
The consumer will not accept a batch with a large number of defectives.
On the other hand, the producer does not want to reject a batch with a small number of defectives.
A producer does not want to test everything produced, as that is impractical and inefficient, and (in cases where testing necessarily destroys the merchandise in some way) unfeasible.
Hence a sample is tested.
The aim of acceptance sampling is to:
- $(1): \quad$ minimise the sample size with respect to the batch size
- $(2): \quad$ minimise the producer's risk
- $(3): \quad$ minimise the consumer's risk
The maximum number $d_{\mathrm {max} }$ of allowed defectives in a given sample is determined in order to achieve an optimal solution.
Economic factors which influence the sample size taken and the optimum values of the producer's risk and consumer's risk include:
- Production costs
- Cost of rectification of faulty items
- Cost of scrapping or selling faulty items or rejected batches at a lower price.
Examples
Sample Size $200$
Let the sample size be $200$.
Let the rule be to accept a batch for which the number of defectives $d$ is such that $d \le 3$.
Let the producer's risk $\alpha$ be the probability of the consumer rejecting a batch with $0 \cdotp 5 \%$ or less defectives.
Let the consumer's risk $\beta$ be the probability of the consumer accepting a batch with $5 \%$ or more defectives.
Then:
| \(\ds \alpha\) | \(=\) | \(\ds 0 \cdotp 019\) | ||||||||||||
| \(\ds \beta\) | \(=\) | \(\ds 0 \cdotp 009\) |
Also see
- Results about acceptance sampling can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): acceptance sampling
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): acceptance sampling