Question $2$

$($a$)($i$)$ In terms of variation, what is meant by the term $$in statistical control$?(3$ marks$)$

$($ii$)$If a process is $$out of specification$,$ then by definition, it is also out of statistical control$$

Explain whether or not this statement is true. Justify your answer clearly $(3$ marks$)$

$($b$)$ An international company who produce precision$-$cut wire to be used in computer assembly have

recently taken sub$-$groups of four pieces from the process$---$ every hour for the past $24$ hours. The

mean wire length $($inches$)$ and range values of each of these sub$-$groups are recorded in Table $2\mathrm{.}0.$

Based on the available data;

$($i$)$ Determine the set of Warning and Action Limits for the Mean Chart $(2$ marks$)$

$($ii$)$ Determine the Action Limit for the Range Chart $(2$ marks$)$

$($iii$)$ Draw the first twelve points on Mean Control Chart for this process $(4$ marks$)$

$($iv$)$ List $3$ of the criteria which are indicative of an $$out of control$$ process $(3$ marks$)$

$($v$)$ Stating your reasons, determine whether or not the points drawn in part $($iii$)$ indicate

that the process is $$out of control$(2$ marks$)$

Note: Control Chart Constants are listed in