A standard of 0.3 ppm has been established for formaldehyde emission levels in wood products. Suppose that the standard deviation of emissions in an individual board is. Any lot that contains 1% of its items above 0.3 ppm is considered acceptable. Any lot that has 8% or more of its items above 0.3 ppm is considered unacceptable. Good lots are to be accepted with probability 0.95, and bad lots are to be rejected with probability 0.90.
a. Using the 1% nonconformance level as an , and assuming that lots consist of 5,000 panels, find an appropriate set of sampling plans from , assuming is unknown.
b. Find an attributes-sampling plan that has the same curve as the variables sampling plan derived in part (a). Compare the sample sizes required for equivalent protection. Under what circumstances would variables sampling be more economically efficient?
c. Using the 1% nonconforming as an , find an attributes sampling plan from . Compare the sample sizes and the protection obtained from this plan with the plans derived in parts (a) and (b).