$[$LO$2$:$10\%$; LO$3$: $10\%$;$LO4$:$10\%$ Topic: Analysis of Variance

In Analysis of Longitudinal Data, $2$nd ed$.,(2002,$ Oxford University Press$),$ by Diggle,

Heagerty, Liang, and Zeger, the authors analyze the effects of three types of cow feed on the

protein content of cow's milk. The data presented below are observations over a one$-$week

period of $25$ cows fed either jali or barley and $27$ cows each fed the other two types of

feed:

$($a$)$ Does the type of cow feed affect the protein content of cow's milk? Make a graph using

statistical processing software to determine the differences between the three types of cow feed

on the protein content of cow's milk.

$($b$)$ Perform a variance analysis using $=0\mathrm{.}05$ and determine the P $-$value of the test, what

decision do you get from the results of the test?

$($c$)$ Determine which feed has a significant difference between one feed and another, if the

significance level is $5\%?[$LO$2$:$10\%$; LO$4$:$10\%]$ Topic: Factorial Design of Experiments

a$.$ Explain what is meant by Design of Experiments and $2$ k Factorial Design?

b$.$ Explain the assumptions, data type requirements and data analysis formulas for

designing an experiment!

c$.$ Mention how many types of factorial designs for this data and if a researcher wants to

analyze the data, explain the steps or basic formulas related to the concept of the data

analysis stages!

i$.$ An engineer is interested in seeing the effects of cutting speed $($A$),$ metal

hardness $($B$),$ and cutting angle $($C$)$ on the service life of the cutting tool.

ii$.$ The R&D Team of a Semiconductor Manufacturing Company wants to know the

results of the following factors with each at two levels, namely Factors $($and levels$)$

are $A=$ aperture setting $($small$,$ large$)$; $B=$ exposure time below nominal,

$20\%$ above nominal$)$; $C=$ development time $(30$ and $45$ seconds$)$; $D=$ mask

dimensions $($small$,$ large$)$; and $E=$ etch time $(14\mathrm{.}5$ and $15\mathrm{.}5$ minutes$).3.[$LO$3$:$10\%$; LO$4$:$20\%]$ Topic: Statistical Quality Control

In an automotive engine manufacturing company, samples of $200$ engines were observed to calculate the number of defect points. The following is the data for the $20$ samples.

$\backslash$table$[[$Sample$,\backslash$table$[[$No$.$ of$],[$Defectives$]],$Sample,$\backslash$table$[[$No$.$ of$],[$Defectives$]]],[1,44,11,52],[2,63,12,74],[3,40,13,43],[4,35,14,50],[5,29,15,60],[6,56,16,38],[7,40,17,36],[8,38,18,65],[9,74,19,41],[10,66,20,95]]$

a$.$ Create a P$-$chart for this process. Is the process still within the lower and upper limits controlled by statistical control?

b$.$ Suppose the sample is only $100,$ pcs$.$ Use the table data to create a P$-$chart diagram for this process. Revise the lower and upper limits of statistical control limits if necessary

c$.$ Compare the control limits in parts $($a$)$ and $($b$).$ Explain why they are different? $4.$Topic: Statistical Quality Control

A shipbuilding industry is taking specification data for the outer diameter of the hub, which is $60\mathrm{.}3265+-0\mathrm{.}001mm.$ A random sample of size $n=20$ is taken and the data is shown in the following table:

$\backslash$table$[[$Sample$,$x$,$Sample,x$],[1,60\mathrm{.}3262,11,60\mathrm{.}3262],[2,60\mathrm{.}3262,12,60\mathrm{.}3262],[3,60\mathrm{.}3262,13,60\mathrm{.}3269],[4,60\mathrm{.}3266,14,60\mathrm{.}3261],[5,60\mathrm{.}3263,15,60\mathrm{.}3265],[6,60\mathrm{.}3260,16,60\mathrm{.}3266],[7,60\mathrm{.}3262,17,60\mathrm{.}3265],[8,60\mathrm{.}3267,18,60\mathrm{.}3268],[9,60\mathrm{.}3263,19,60\mathrm{.}3262],[10,60\mathrm{.}3269,20,60\mathrm{.}3266]]$

$($a$)$ Construct a control chart for the individual measurements of the sample. Calculate the control limits$.$ Explain what conclusions you draw from these measurements.

$($b$)$ Compare your chart in part $($a$)$ with a chart that uses only the last $($least significant$)$ digit of each diameter as the measurement. Explain your conclusions.

$($c$)$ Estimate $$ and $$ from the revised range of motion and use these values to estimate PCR and PCRk$!$

$($d$)$ Explain the interpretation of these ratios. mana saja yang menunjukkan perbedaan?