Question

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.

a- use Procedure II (M method)

please solve manually with details

Answer 1

We have the following plan parameters:

p₁ = 0.02, p₂ = 0.1,

The two points of the OC curve are:

Now the required sample size for the variables sampling plan is gien by:

The critical value is given by:

k = LSL + = 1.71558

Thus we accept the lot iff,

Here

Thus we accept the lot.

The OC curve for this sampling plan is given by:

From the OC curve we can measure that the probability of accepting lots which are 5% defective is 0.377.