A construction engineer buys steel cable in large rolls to use in supporting equipment and temporary structures during the process of erecting permanent structures. Specifications require the breaking strength of the steel cable to exceed 200 pounds. For a lot size of 1,500 large rolls of steel cable, consider an acceptance sampling plan based on a sample of n = 20 rolls and acceptance number a = 2.

a. Find the producer’s risk if the AQL is .05.

b. Find the consumer’s risk if the lot fraction failing to meet breaking strength specifications is p₁ = .10.

c. Draw a rough sketch of the operating characteristic curve for the sampling plan. Is the sampling plan reasonable?

d. Find the appropriate MIL-STD-105D normal (level) general inspection sampling plan for a lot size of 1,500 large rolls of steel cable and an AQL of .05.

e. Refer to part d. Find the producer’s risk under the inspection sampling plan. (Hint: Use the normal approximation to the binomial.)

f. Refer to part d. Find the consumer’s risk if the lot fraction failing to meet breaking strength specifications is p₁ = .08.