Control charts for and R are in use with the following parameters:

Chart R Chart

UCL $=363\mathrm{.}0$ UCL $=16\mathrm{.}18$

Center line $=360\mathrm{.}0$ Center line $=8\mathrm{.}91$

LCL $=357\mathrm{.}0$ LCL $=1\mathrm{.}64$

The sample size is n $=9.$ Both charts exhibit control.

The quality characteristic is normally distributed.

$($a$)$ What is the a$-$risk associated with the chart?

$($b$)$ Specifications on this quality characteristic are

$358\backslash$pm $6.$ What are your conclusions regarding the

ability of the process to produce items within

specifications?

$($c$)$ Suppose the mean shifts to $357.$ What is the

probability that the shift will not be detected on

the first sample following the shift?