Acceptance Sampling: Calculating the Likelihood 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 likelihood of accepting a lot that is 1% defective can be calculated using the binomial distribution formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Where:

• n is the sample size (20 in this case)
• k is the number of defective parts allowed (1 in this case)
• p is the proportion of defective parts in the lot (0.01 or 1%)

Plugging in the values:

P(X = 1) = (20 choose 1) * 0.01^1 * (1-0.01)^(20-1) P(X = 1) = 20 * 0.01 * 0.8187 P(X = 1) = 0.1637

Therefore, the likelihood of accepting a lot that is 1% defective is 16.37%.