ITPEC FE Subject A October 2025 Question 58
The horizontal and vertical axes of an Operating Characteristic (OC) curve in quality management generally represent the percent defective of a lot and the success rate of a lot, respectively. Samples of size n are extracted from a lot of size N. When the number of defective samples is less than or equal to the pass quantity C, the lot is considered to have passed; otherwise, it is considered to have failed.
Which of the following is a diagram that shows the trend of change in the OC curve when N and n are fixed and C takes the values 0, 1, and 2?
Explanation
C = 0 on the left, then C = 1, then C = 2 on the right, never crossing — a larger pass quantity accepts lots at a higher percent defective.
For a given percent defective, the lot passes when the sample holds at most C defectives. Allowing one or two defectives instead of none adds outcomes that pass, so at every percent defective above 0 the success rate for C = 2 is higher than for C = 1, which is higher than for C = 0.
All three curves start at 100% when the lot has no defectives and fall towards 0, but the larger C, the further right the curve lies, and the curves never meet again. With C = 0 one defective fails the lot, so that curve drops at once; with larger C it stays high for a while first. Diagram (b) shows exactly this.
Answer (b)
Why not others:
- •(a) — the same curves with the labels reversed, so C = 0 would pass more lots than C = 2 at the same percent defective, the opposite of a looser pass rule
- •(c) — the order is right, but the three curves meet at a point with a positive percent defective, where a larger C must always give a strictly higher success rate
- •(d) — the curves meet in the same way as in (c), and the labels are reversed as well
Key rule: On an OC curve, raising the pass quantity C or shrinking the sample size n moves the curve right: more lots pass at each percent defective.
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