Acceptance Sampling: Understanding the Probability of Accepting a 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?

The probability of accepting a lot that is 1% defective can be calculated using the binomial distribution formula:

P(X = 0) + P(X = 1)

Where X is the number of defective parts in a sample of 20 and P(X) is the probability of X defects in the sample.

P(X = 0) = (0.99)^20 = 0.8179 P(X = 1) = 20(0.01)(0.99)^19 = 0.1629

Therefore, the likelihood of accepting a lot that is 1% defective is:

P(X = 0) + P(X = 1) = 0.8179 + 0.1629 = 0.9808 or 98.08%