A single-sampling plan using a sample size of 50 on a lot size of 2,000 has the following performance:
$$\begin{array} { | c | c | }
\hline \begin{array} { c }
\text { Proportion } \
\text { Defective }
\end{array} & \begin{array} { c }
\text { Probability of } \
\text { Acceptance }
\end{array} \
\hline 0.01 & 0.98 \
\hline 0.02 & 0.95 \
\hline 0.03 & 0.90 \
\hline 0.04 & 0.74 \
\hline 0.05 & 0.41 \
\hline 0.06 & 0.15 \
\hline
\end{array}$$
Today the company making the purchase receives two lots of 2,000 items and the inspection department is in a big hurry.Which action will result in an identical AOQL for the purchasing company?
A) Take a random sample of 25 from each lot and accept or reject both lots based on the results.
B) Take a random sample of 50 from one lot and accept or reject the second lot based on the first lot's results.
C) Take a random sample of 100 from one lot and accept or reject the second lot based on the first lot's results.
D) Take a random sample of 50 from each lot and accept or reject each lot based on the results.

Question

A single-sampling plan using a sample size of 50 on a lot size of 2,000 has the following performance:
$$\begin{array} { | c | c | } 
\hline \begin{array} { c } 
\text { Proportion } \
\text { Defective }
\end{array} & \begin{array} { c } 
\text { Probability of } \
\text { Acceptance }
\end{array} \
\hline 0.01 & 0.98 \
\hline 0.02 & 0.95 \
\hline 0.03 & 0.90 \
\hline 0.04 & 0.74 \
\hline 0.05 & 0.41 \
\hline 0.06 & 0.15 \
\hline
\end{array}$$
Today the company making the purchase receives two lots of 2,000 items and the inspection department is in a big hurry.Which action will result in an identical AOQL for the purchasing company?
A) Take a random sample of 25 from each lot and accept or reject both lots based on the results.
B) Take a random sample of 50 from one lot and accept or reject the second lot based on the first lot's results.
C) Take a random sample of 100 from one lot and accept or reject the second lot based on the first lot's results.
D) Take a random sample of 50 from each lot and accept or reject each lot based on the results.

Quizplus · Accepted Answer

To achieve the same average outgoing quality limit (AOQL) as the single-sampling plan with a sample size of 50 on a lot size of 2,000, we need to choose a sampling plan with similar probabilities of acceptance for a given proportion of defective items. 
Option D is the only choice that uses a sample size of 50 for each lot, which is the same total sample size used in the original single-sampling plan. Therefore, option D is the best choice to achieve a similar AOQL. Options A, B, and C all have different sample sizes and therefore have different probabilities of acceptance for a given proportion of defective items, leading to different AOQLs.

A Single-Sampling Plan Using a Sample Size of 50 on a Lot