The only way to realize the ideal OC curve is 100% inspection. With sampling, we can come
close. In general, as the sample size increases, keeping the acceptance number proportional, the
OC curve approaches the ideal, as shown in Figure 3.
Similarly, as the acceptance number, c, gets larger for a given sample size, n, the OC curve
approaches the ideal. Figure 4 illustrates the relationship.
Some Specific Points on the OC Curve
Because sampling doesn’t allow the ideal OC curve, we need to consider certain risks. The first
risk is that the consumer will reject a lot that satisfies the established conditions, i.e., the process
quality is acceptable, but, by the luck of the draw, there are too many nonconforming items in the
sample. This is called the producer’s risk, and is denoted by the Greek letter α.
The second risk is that the consumer will accept a lot that doesn’t meet the conditions, i.e., by the
luck of the draw there are not many nonconforming items in the sample, so the lot is accepted.
This is the consumer’s risk and is denoted by the Greek letter β.
The literature contains a variety of typical values for α and β, but common values are 5% and
10%. When we locate these values on the OC curve, expressed in terms of probability of
acceptance, we actually locate 1 – α