Suppose that x̅ and R charts based on subgroups of size 3 are used to monitor the moisture content of a type of paper. The x̅ and R charts are found to be in statistical control with x̅̅ = 6.0 percent and R̅ = .4 percent. Further, a histogram of the individual moisture content readings suggests that these measurements are approximately normally distributed.
a. Compute the natural tolerance limits (limits that contain almost all the individual moisture content readings) for this process.
b. If moisture content specifications are 6.0 percent 6.5 percent, is this process capable of meeting the specifications? Why or why not?
c. Estimate the fraction of paper that is out of specification.
d. Find the sigma level capability of the process.