Question

Consider an acceptance sampling plan with N=20 and C=0. Compute the producer's risk for each of the following cases.

a. The lot has a defect rate of 2% (to 4 decimals).

P (Accept lot):


Producer's risk:


b. The lot has a defect rate of 6% (to 4 decimals).

P (Accept lot):


Producer's risk:

Answer 1

The producer's risk represents the probability of rejecting a lot that is good. It is calculated using the cumulative binomial distribution formula in acceptance sampling.

Step-by-step explanation:

The producer's risk represents the probability of rejecting a lot that is good. In acceptance sampling, the producer's risk is calculated using the cumulative binomial distribution.

a. The lot has a defect rate of 2%. To compute the producer's risk, we need to determine the probability of accepting the lot, which is the probability of having 0 or 1 defectives in the sample of 20. Using the cumulative binomial distribution formula, we find that P(Accept lot) = P(X ≤ 1) = P(X=0) + P(X=1) = C(20,0)(0.02^0)(0.98^20) + C(20,1)(0.02^1)(0.98^19).

b. The lot has a defect rate of 6%. Similarly, we calculate the probability of accepting the lot as P(X ≤ 1) = P(X=0) + P(X=1) = C(20,0)(0.06^0)(0.94^20) + C(20,1)(0.06^1)(0.94^19).