pplication $1$: Control Charts for Variables

Webster Chemical Company produces mastics and caulking for the construction industry.

The product is blended in large mixers and then pumped into tubes and capped.

Webster is concerned whether the filling process for tubes of caulking is in statistical

control. The process should be centered on $8$ ounces per tube. Several samples of eight

tubes are taken and each tube is weighed in ounces.

Tube Number

Sample $12345678$ Avg Range

$17\mathrm{.}988\mathrm{.}348\mathrm{.}027\mathrm{.}948\mathrm{.}367\mathrm{.}687\mathrm{.}818\mathrm{.}11$

$28\mathrm{.}238\mathrm{.}127\mathrm{.}988\mathrm{.}418\mathrm{.}318\mathrm{.}187\mathrm{.}998\mathrm{.}06$

$37\mathrm{.}897\mathrm{.}777\mathrm{.}918\mathrm{.}048\mathrm{.}007\mathrm{.}897\mathrm{.}938\mathrm{.}09$

$48\mathrm{.}248\mathrm{.}187\mathrm{.}838\mathrm{.}057\mathrm{.}908\mathrm{.}167\mathrm{.}978\mathrm{.}07$

$57\mathrm{.}878\mathrm{.}137\mathrm{.}927\mathrm{.}998\mathrm{.}107\mathrm{.}818\mathrm{.}147\mathrm{.}88$

$68\mathrm{.}138\mathrm{.}148\mathrm{.}118\mathrm{.}138\mathrm{.}178\mathrm{.}128\mathrm{.}138\mathrm{.}14$

Assuming that taking only $6$ samples is sufficient, is the process in statistical control?

Conclusion on process variability?

UCLR $=$

LCLR $=$

Conclusion on process average?

UCLx $=$

LCLx $=$