Question

When acceptance number of a single sampling plan under attribute category is zero with sample size less than or equal to 10, the Operating Characteristic (OC) curve is

• A. A horizontal line
• B. A vertical line
• C. A convex function
• D. An inverted S-shaped curve

Hint:

For small sample sizes with a zero acceptance number, the OC curve is convex, showing rapid rejection as the proportion of defectives increases.

Answer 1

The Correct Option is C

In acceptance sampling, the Operating Characteristic (OC) curve describes the probability of acceptance as a function of the proportion defective in the lot. When the acceptance number is zero and the sample size is small (less than or equal to 10), the OC curve behaves in a very specific way.
Step 1: For a single sampling plan, if the acceptance number is zero, it means that any defect in the sample leads to rejection of the lot. For small sample sizes (e.g., 10), the OC curve is not an S-shape but rather a convex function. This is because the probability of accepting the lot sharply decreases as the proportion defective increases, and the curve is steep for low defect levels.
Step 2: An S-shaped curve generally corresponds to larger sample sizes, where the curve smoothly transitions from acceptance to rejection. But in this case, with zero acceptance and small sample size, the OC curve is convex, representing a sharp decrease in acceptance probability with the increase in defect proportion.
Thus, the correct answer is (C).