Assignment:
For the single sampling plan derived in part (a) of Problem below, suppose lots that are not passed are returned to Hammerhead.
a. Estimate the graph of the AOQ curve by computing AOQ(p) for various values of p.
b. Using the results of part (a), estimate the maximum proportion of defective nails that Modulo will be using in its construction.
Q1. Hammerhead produces heavy-duty nails, which are purchased by Modulo, a maker of prefabricated housing. Modulo buys the nails in lots of 10,000 and subjects a sample to destructive testing to determine the acceptability of the lot. Modulo has established an AQL of 1 percent and an LTPD of 10 percent.
a. Assuming a single sampling plan with n = 100 and c = 2, find α and β.
b. Derive the sequential sampling plan that achieves the same values of α and β as the single sampling plan derived in part (a).
c. By estimating the ASN curve, find the maximum value of the expected sample size Modulo will require if it uses the sequential plan derived in part (b).
d. Suppose that the sequential sampling plan derived in part (b) is used. One hundred nails are tested with the following result: The first 80 are acceptable, the 81st is defective, and the remaining 19 are acceptable. By graphing the acceptance and the rejection regions, determine whether the sequential sampling plan derived in part (b) would recommend acceptance or rejection on or before testing the 100th nail.
Provide complete and step by step solution for the question and show calculations and use formulas.