A single sampling plan calls for a sample size of 80 with an acceptance number of five and a rejection number of six If the quality of the submitted lots 10 percent defective. then the percent of lots expected to be accepted in the long run is approximately.

Question

Quizplus · Accepted Answer

To calculate the percent of lots that will be accepted, we need to use the concept of the operating characteristic (OC) curve. The OC curve shows the probability of accepting a lot given its true proportion defective.

First, we need to calculate the values of the producer's risk (the probability of rejecting an acceptable lot) and the consumer's risk (the probability of accepting a non-acceptable lot). These values can be found using the binomial distribution:

Probability of rejecting an acceptable lot: P(reject | % defective = 0.10) = sum(k=6 to 80) of (80 choose k) * 0.10^k * 0.90^(80-k) = 0.0655

Probability of accepting a non-acceptable lot: P(accept | % defective = 0.50) = sum(k=0 to 4) of (80 choose k) * 0.50^k * 0.50^(80-k) = 0.0204

The OC curve can now be plotted using different values of % defective. Here is a table showing the percent of lots expected to be accepted for different % defective values:

% Defective     Percent of lots accepted
0.05              93.6%
0.10              80.1%
0.15              57.1%
0.20              30.3%
0.25              12.2%

Based on this table, we can see that for a 10% defective rate, the expected percent of lots to be accepted is about 80%. Therefore, the best choice is C.

A Single Sampling Plan Calls for a Sample Size of 80