Problem: SlimCase

A company making smartphone cases is concerned about the exact length of their cases. The company has a lower specification limit of $12\mathrm{.}75$ cm and an upper specification limit of $13\mathrm{.}25$ cm$.$ The standard deviation is $0\mathrm{.}125$ cm and the mean is $13$ cm$.$

$1.$

Question $1$

What is the process capability index for the process?

$($Your answer should be formatted as a decimal $-0\mathrm{.}00)$

$1$ point

Enter answer here

$2.$

Question $2$

What is the probability that a smartphone case falls outside the specification limits$?$

$1$ point

Enter answer here

$3.$

Question $3$

If the company aims to produce $80,000$ non$-$defective cases every month, how many cases should it produce in total? Assume that rework is not possible. Round up to the next largest integer number.

$($Your answer should be formatted $00,000$ or $00000)$

$1$ point

Enter answer here

$4.$

Question $4$

The company now wants to reduce its defect probability and run a $$Six Sigma Process$.$ To what level would they have to reduce the standard deviation in the process to meet this target?

$($Write answer as a decimal $0\mathrm{.}0000$ or $0\mathrm{.}00000)$

Problem: BestStuff

Mark is a newly minted quality engineer at BestStuff Inc. His boss, intending to promote higher qualityin the company, tells him to increase the process capability index of their main product. To this end, Mark decides to increase the upper specification limit and reduce the lower specification limit$.$

$5.$

Question $5$

What happens as a consequence?

$3$ extra credit points

The process capability index does not increase, because the process capability index would only change if the control limits were changed.

The process capability index does increase, which is why the process quality is reduced.

The process capability index does not increase, because the variation in the process is unchanged.

The process capability index does increase, though one might question if the underlying process is really better.

More data is needed to answer the question.