Acceptance Sampling: Probability of Accepting a 1% Defective Lot

Acceptance sampling is a statistical method used to monitor the quality of purchased parts and components. To ensure the quality of incoming parts, a purchaser or manufacturer normally samples 20 parts and allows 1 defect.

What is the likelihood of accepting a lot that is 1% defective?

Assuming a one-sided acceptance sampling plan with a sample size of 20 and 1 defect allowed, the acceptance quality limit (AQL) is 5%. This means that if the lot is 5% defective or less, it will be accepted; otherwise, it will be rejected.

However, in this case, the lot is only 1% defective. Therefore, the probability of accepting the lot is very high. To calculate the exact probability, we can use the binomial distribution:

P(X ≤ 1) = P(X = 0) + P(X = 1)

where X is the number of defects in a sample of 20.

P(X = 0) = (0.99)^20 = 0.817

P(X = 1) = 20(0.99)^19(0.01) = 0.174

Therefore, the probability of accepting the lot is:

P(X ≤ 1) = 0.817 + 0.174 = 0.991

So, the likelihood of accepting a lot that is 1% defective is very high, at 99.1%.