Analytics Exercise Tesla: Case Part B: Quality Control Analytics

$1.$ If the specification is such that no washer should be greater than $2\mathrm{.}4$millimeters, assuming that the thickness are distributed normally, what fraction of the output is expected to be greater than this thickness

$2.$ If there are upper and lower specifications, where the upper thickness limit is $2\mathrm{.}4$ and the lower thickness limit is $1\mathrm{.}4,$ what fraction of the output is expected to be out of tolerance?

$3.$ What is the Cpk for the process?

$4.$ What would be the Cpk for the process if it were centered between the specification limits $($assume the process standard deviation is the same$)?$

$5.$ What percentage of output would be expected to be out of tolerance if the process were centered?

$6.$ Set up xbar and range control charts for the current process. Assume the operators will take samples of $10$ washers at a time.

$7.$ Plot the data on your control charts. Does the current process appear to be in control?

$8.$ If the process could be improved so that the standard deviation were only about $0\mathrm{.}10$ millimeter, what would be the best that could be expected with the process relative to the fraction defective?