Acceptance Sampling: Calculating the 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?

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

P(X ≤ 1) = C(20,0)(0.01)^0(0.99)^20 + C(20,1)(0.01)^1(0.99)^19

where X is the number of defective parts in the sample, C(20,0) and C(20,1) are the binomial coefficients, and (0.01)^0 and (0.01)^1 are the probabilities of no defects and one defect, respectively. (0.99)^20 and (0.99)^19 are the probabilities of no defects and one defect, respectively.

Simplifying the formula, we get:

P(X ≤ 1) = (1)(0.99)^20 + (20)(0.01)*(0.99)^19

P(X ≤ 1) = 0.1818

Therefore, the likelihood of accepting a lot that is 1% defective is 18.18%.