Quality control: Acceptance sampling
Operations characteristic curves for sampling plans with sampling by attributes
are considered. A singlesampling plan is considered. The sampling distribution
for the singlesampling 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

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 OCcurve 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 OCcurve 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 OCcurve 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 OCcurve 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
