The density of a plastic part used in a cellular telephone is required to be at least 0.70 g/cm3. The parts are supplied in large lots, and a variables sampling plan is to be used to sentence the lots. It is desired to have p1 = 0.02, p2 = 0.10,α = 0.10, and β = 0.05. The variability of the manufacturing process is unknown but will be estimated by the sample standard deviation.
LSL = 0.70 g/cm3, p1 = 0.02; 1 – a = 1 – 0.10 = 0.90; p2 = 0.10; β = 0.05
(a) Find an appropriate variables sampling plan, using Procedure 1.
(b) Suppose that a sample of the appropriate size was taken, and x  0.73 and s 1.05102. Should the lot be accepted or rejected?
(c) Sketch the OC curve for this sampling plan. Find the probability of accepting lots that are 5% defective.