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 σ = 0.10 ppm. 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.
target = 3ppm;  = 0.10ppm; p1 = 1% = 0.01; p2 = 8% = 0.08
(a) Derive a variables-sampling plan for this situation.
(b) Using the 1% nonconformance level as an AQL, and assuming that lots consist of 5,000 panels, find an appropriate set of sampling plans from MIL STD 414, assuming σ is unknown. Compare the sample sizes and the protection that both producer and consumer obtain from this plan with the plan derived in part (a).
(c) Find an attributes sampling plan that has the same OC curve as the variables sampling plan derived in part