Acceptance Sampling: How Likely Is It To Accept 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?

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 defects in a sample of 20 parts and P(X = 0) is the probability of no defects and P(X = 1) is the probability of one defect.

P(X = 0) = (0.99)^20 = 0.8179 P(X = 1) = 20C1 * (0.99)^19 * (0.01)^1 = 0.1712

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

0.8179 + 0.1712 = 0.9891 or approximately 98.91%