QI$.($Quality$)$ Consider the following potential quality problems:

$$ Wine that is served in a restaurant sometimes is served too warm, while at other times it is served too cold.

$$ A surgeon in a hospital follows the hygiene procedures in place on most days, but not all days.

$$ A passenger traveling with an airline might be seated at a seat with a defective audio system.

$$ An underwriter in a bank might sometimes accidentally approve loans to consumers that are not creditworthy.

For each of these potential problems:

a$)$ What type of data would you collect?

b$)$ What type of control charts would you use?

Q$2.$ Syska Long Life $75-$watt light bulbs are designed to have a life of $1125$ hours with tolerances of $\backslash$pm $210$ hours. The process that makes light bulbs has a mean of $1050$ hours, with a standard deviation of $55$ hours. Compute the process capability ratio $($Cp$)$ and the process capability index $($Cpk$),$ and comment on the overall capability of the process.

Explain to what extent the process for producing Syska Long Life bulbs would have to be improved in order to achieve $6-$sigma quality.

Q$3.$ The Stryker Baseball Bat Company manufactures wooden and aluminum baseball bats at its plant in New England. Wooden bats produced for the mass market are turned on a lathe, where a piece of wood is shaped into a bat with a handle and barrel. The bat is cut to its specified length and then finished in subsequent processes. Once bats are cut to length, it is $[5)$

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difficult to rework them into a different style, so it is important to catch defects before this step. As such, bats are inspected at this stage of the process. A specific style of wooden bat has a mean barrel circumference of $9$ inches at its thickest point with a standard deviation of

$0\mathrm{.}6$ inch. $($The process variability is assumed to be normally distributed.$)$

a$)$ Construct a mean control chart for this process for $30$ limits and a sample size of $10$ bats.

b$)$ Three samples are taken, and they have average bat diameters of $9\mathrm{.}05$ inches, $9\mathrm{.}10$ inches, and $9\mathrm{.}08$ inches. Is the process in control?

c$)$ What effect will increasing the sample size to $20$ bats have on the control charts? Will the conclusions reached in part $($b$)$ change for this sample size?