Thermostats are subjected to rigorous testing before they are shipped to air conditioning

technicians around the world. Results from the last five samples are shown in the table. Create

control charts that will fully monitor the process and indicate the result of X$-$bar and R chart

analysis.

Unit # Sample $1$ Sample $2$ Sample $3$ Sample $4$ Sample $5$

$173\mathrm{.}570\mathrm{.}872\mathrm{.}273\mathrm{.}671\mathrm{.}0$

$271\mathrm{.}371\mathrm{.}073\mathrm{.}172\mathrm{.}772\mathrm{.}2$

$370\mathrm{.}072\mathrm{.}671\mathrm{.}972\mathrm{.}473\mathrm{.}3$

$471\mathrm{.}170\mathrm{.}670\mathrm{.}374\mathrm{.}273\mathrm{.}6$

$570\mathrm{.}870\mathrm{.}770\mathrm{.}773\mathrm{.}571\mathrm{.}1$

A$)$ x bar and r chart are both out of control

B$)$ x bar chart is in control but r chart is out of control

C$)$ x bar chart is out of control but r chart is in control

D$)$ x bar and r chart are both in control

$4)$ The defect rate for a product has historically been about $5\mathrm{.}0\%.$ What is the upper control chart

limit if you wish to use a sample size of $50$ and $3-$sigma limits$?$

A$)0\mathrm{.}082$

B$)0\mathrm{.}112$

C$)0\mathrm{.}142$

D$)0\mathrm{.}172$

Problems $5$ and $6$ uses same data table.

$5)$ Samples of $100$ checks each were taken at a bank from an encoding machine $($which records

the amount of a check$)$ over a five$-$day period. Details are summarized in the table below. If the

bank were to use the average proportion defective from these five samples as the central line for

a process control chart, what would be the central line? $($use $3$ sigma$)$

Sample Number Number Defective

$11$

$24$