Table $1$

Factors for Calculating Three$-$Sigma Limits for the Chart and R$-$Chart

Size of

Sample

$($n$)$ Factor for UCL and LCL for

x$-$bar$-$Charts

A$2$ Factor for

LCL for

R$-$Charts

D$3$ Factor for

UCL for

R$-$Charts

D$4$

$21\mathrm{.}88003\mathrm{.}267$

$31\mathrm{.}02302\mathrm{.}575$

$40\mathrm{.}72902\mathrm{.}282$

$50\mathrm{.}57702\mathrm{.}115$

$60\mathrm{.}48302\mathrm{.}004$

$70\mathrm{.}4190\mathrm{.}0761\mathrm{.}924$

$80\mathrm{.}3730\mathrm{.}1361\mathrm{.}864$

$90\mathrm{.}3370\mathrm{.}1841\mathrm{.}816$

$100\mathrm{.}3080\mathrm{.}2231\mathrm{.}777$

Company B manufactures Thermostats. 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 below. Calculate control limits for a chart that will monitor performance to target.

The correct control limits as $($LCL$,$UCL$)$ are:

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

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

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

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

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

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