The GATE Grind

GATE 2021 PI – Question 13

Quality and Reliability · Quality Management · 1 mark · Multiple choice

For a single-sampling attribute plan with acceptance number zero and sample size at most ten, which form describes the operating-characteristic curve?

  1. Horizontal line
  2. Vertical line
  3. Convex function
  4. Inverted S-shaped curve

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Show answer and explanation

Correct answer: (C) Convex function

Explanation

Under the binomial model, lot acceptance requires zero sample defects: $P_a=(1-p)^n$. Its second derivative is $n(n-1)(1-p)^{n-2}\ge0$, so the curve is convex, **C**. For n = 1 it is linear, which is also convex.

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