Question #$6(16$ points$)$

We make two different sizes of home replacement windows on the same production

line. The target value $($or nominal value$)$ for the length of each window is $24$ and $28$

inches, respectively. Since few people have homes requiring these sizes of windows, we

only make twenty windows each week. The target values and average ranges $($for

samples of size $4)$ are given in the table below. To simplify the monitoring process, we

would like to use one set of charts to monitor this production line.

Size of window

$24"$ Model

$28"$ Model

Target $($or nominal$)$ value

$28"$

Average range

$0\mathrm{.}08"$

$0\mathrm{.}04"$

$($a$)$ What are the UCL, LCL$,$ and Centerline of the appropriate control charts,

assuming the standard deviations of the length of each window type are not the

same? $(8$ Points$)$

$($b$)$ For the two samples of size $4$ given below is the process statistically in control? $(8$

Points$)$

Sample

$1$

$2$

Part

$24"$ Model

$28"$ Model

Mean

$24\mathrm{.}07"$

$27\mathrm{.}98"$

Range

$0\mathrm{.}06"$

$0\mathrm{.}02"$ Question $\backslash$#$6(16$ points$)$

We make two different sizes of home replacement windows on the same production line. The target value $($or nominal value$)$ for the length of each window is $24$ and $28$ inches, respectively. Since few people have homes requiring these sizes of windows, we only make twenty windows each week. The target values and average ranges $($for samples of size $4)$ are given in the table below. To simplify the monitoring process, we would like to use one set of charts to monitor this production line.

$($a$)$ What are the UCL, LCL$,$ and Centerline of the appropriate control charts, assuming the standard deviations of the length of each window type are not the same? $(8$ Points$)$

$($b$)$ For the two samples of size $4$ given below is the process statistically in control? $(8$ Points$)$