While a sampling plan meets our requirements for the extreme values of good and bad quality, we cannot readily determine how well the plan discriminates between good and bad lots at intermediate values. For this reason, sampling plans are generally displayed graphically through the use of Operating Characteristic (OC) curves. These curves, which are unique for each combination of n and c, simply illustrate the probability of accepting lots with varying percentages of defectives.
Shaping the OC Curve: A sampling plan discriminating perfectly between good and bad lots has an infinite vertical slope at the selected value of AQL. Any percentage defective to the left of 2% would always be accepted, and those to the right, always rejected. However, such a curve is possible only with complete inspection of all units and thus is not a possibility with a true sampling plan. An OC curve should be steep in the region of most interest (between the AQL and the LTPD), which is accomplished by varying n and c. If c remains constant, increasing the sample size n causes the OC curve to be more vertical. While holding n constant, decreasing c also makes the slope more vertical, moving closer to the origin.
