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.
Symbols:
| 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 |
| LTPD |
lot tolerance percentage defective
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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.
Literature:
- Krajewski/Ritzman (1996), Chapter 5
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