Question

Which ONE or MORE among the following options is/are TRUE for the ideal operating characteristics (OC) curve given in the figure?

Note: \( p_0 \) represents the acceptable quality level (AQL) and \( p_1 \) represents the lot tolerance percent defective (LTPD).

• A. Producer's risk is 100%.
• B. Consumer's risk is 100%.
• C. Producer's risk is zero.
• D. Consumer's risk is zero.

Hint:

On the ideal OC curve, acceptance probability is 1 below p0 and 0 above p1, leaving no room for wrongly rejecting good lots or wrongly accepting bad ones.

Answer 1

The Correct Option is C, D

Step 1: Understanding the Question:
The figure shows an ideal OC (operating characteristic) curve, which is the imaginary best-case curve for a sampling plan: it accepts every lot with defect level up to \( p_0 \) with certainty, and rejects every lot with defect level from \( p_1 \) onward with certainty, with a sharp vertical drop in between.
We need to work out what this ideal shape implies for the producer's risk and the consumer's risk.

Step 2: Definitions Needed:
Producer's risk, usually called \( \alpha \), is the chance that a genuinely good lot (defect rate at or below \( p_0 \), the AQL) gets wrongly rejected.
Consumer's risk, usually called \( \beta \), is the chance that a genuinely bad lot (defect rate at or above \( p_1 \), the LTPD) gets wrongly accepted.

Step 3: Reading the Ideal Curve:
From \( p = 0 \) up to \( p = p_0 \), the curve sits flat at a probability of acceptance equal to 1, meaning every good lot in this range is accepted with 100 percent certainty and none are rejected.
Because the probability of rejecting a good lot is zero here, the producer's risk is zero, so option (C) is correct and option (A), which claims 100 percent producer's risk, is wrong.
From \( p = p_1 \) up to \( p = 1 \), the curve sits flat at a probability of acceptance equal to 0, meaning every bad lot in this range is rejected with certainty and none are ever accepted.
Because the probability of accepting a bad lot is zero here, the consumer's risk is zero, so option (D) is correct and option (B), which claims 100 percent consumer's risk, is wrong.

Final Answer:
The ideal OC curve represents a perfect inspection scheme with no sampling error, so both risks vanish. \[ \boxed{\text{Producer's risk} = 0, \ \text{Consumer's risk} = 0 \implies \text{C and D correct}} \]