You have been employed as a quality engineering in a manufacturing company. The

company is producing a moulded part with a nominal diameter of $10$mm with a

tolerance of $\backslash$pm $0\mathrm{.}25$mm$.$ A capability trial has been undertaken and the results show the

average value in a production run of $8$ hours is $10\mathrm{.}08$mm with a standard deviation of

$0\mathrm{.}05$mm$.$

$($i$)$ Using this data, calculate Cpk$,$ Cp & Cpm

$($ii$)$ What is the maximum theoretical capability for the process?

Comment on the values calculated for $($i$)$ and $($ii$)$ above $($is the process capable?$).$ Use

a normal distribution to help explain your answer.