a$.$ Calculate the upper and lower control limits and the center lines for the mean $(\stackrel{}{x})$ and range

$(R)$ charts based on the first $10$ samples when the process is known to be in control. Use the

"factors" given in class slides. $(8$ points$)$

b$.$ Construct the appropriate control chart$($s$)$ showing all $20$ samples $(6$ points$)$

c$.$ Is the process still in control? Why or why not? $(3$ points$)$

Problem $2$

Best Book Stand is a manufacturer of wooden bookstands. The production manager at Best

Book Stand tracks the number of defective book stands out of each lot of $750$ finished products

every week. The following data for $15$ weeks was collected when the production process was

known to be in control.

In order to continuously check if the process is still under control, the manager continued collecting

data for ten more weeks. Again, data indicates the number of defective book stands per lot of

$750$ for each week.

a$.$ Calculate the $3$ upper and lower control limits and the center lines for the proportion of

defective book stands using data from when the process was known to be in control. $(6$ points$)$

b$.$ Construct the appropriate control chart$($s$)$ showing all $25$ samples. $(4$ points$)$

c$.$ Is the process still in control? Why or why not? $(3$ points$)$

Problem $3$

Caman Biscuits produces fruit flavored wafers. The company estimates that each wafer should

be at least $0\mathrm{.}45$ inches and at most $0\mathrm{.}52$ inches thick. The company is considering outsourcing

the wafer production to Warm Biscuits Company. Warm Biscuits produces wafers of normally

distributed thickness with a mean of $0\mathrm{.}48$ inches and standard deviation of $0\mathrm{.}023$ inches. Caman

Biscuits aims for $\frac{+}{-}3$ performance for all its products.

a$.$ Calculate $C_p.$ Is Warm Biscuit's process capable of producing wafers at the performance level

specified by Caman? Please explain your answer. $(3$ points$)$

b$.$ Using $C_{pk},$ check if Warm Biscuit's process is capable of producing wafers at the performance

level specified by Caman? Explain your answer. $(3$ points$)$ Problem $4-$Short Answer

a$.$ Describe the difference between common cause and special cause variation. Provide an

example for each when eating at a restaurant. $(2$ points$)$

b$.$ Describe the four different types of costs associated with quality. Give an example of each for

a doctor's office. $(2$ points$)$Problem $1$

As a brake quality inspector at Cico Friction Products, your primary job is to monitor the average

life of brake shoes being used in the brake assembly. The following sample data on brake shoe

life $($in $1000\text{'}$s of miles$)$ were collected when the production process was known to be in control.

Each sample consisted of $7$ observations:

To cut production costs, Cico recently changed the supplier of a key component. To check if the

supplier change has any impact on brake shoes life, the following $10$ samples were collected after

this change.

take your time there is a lot here