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Quality control: Acceptance sampling

Operations characteristic curves for sampling plans with sampling by attributes are considered. A single-sampling plan is considered. The sampling distribution for the single-sampling plan is the binomial distribution. If the sample size n is greater than 20 and the proportion of defectives p is less than 0.05, the Poisson distribution can be used to approximate the binomial distribution.


c acceptance level
n sample size
N production quantity, lot size (required for the computation of average outgoing quality)
x number of defectives found in a sample
OC operations characteristic curve
AOQ average outgoing quality
Prob probability
AQL acceptable quality level

lot tolerance percentage defective

The shape of the operations characteristic curve may be influenced through changing of n and/or c.

Acceptance level effect:
Decreasing c while holding n constant shifts the OC-curve to the origin and decreases the customer's risk and increases the producer's risk.
Sample size effect:
Decreasing n while holding c constant shifts the OC-curve to the right and decreases the producer's risk and increases the customer's risk.

In order to find n and c for given values of AQL, producer's risk, LTPD and customer's risk, start with c=0 and change n until the OC-curve exhibits the desired producer's risk at the point AQL. Then increase c by 1 and search again for the optimal value of n. Repeat until a OC-curve running close to the points (AQL,producer's risk) and (LTPD, customer's risk).

Alternatively, with button a new module with an automatic search procedure for n and c is displayed.


- Krajewski/Ritzman (1996), Chapter 5

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