Alongside process improvement efforts, Anisha also instituted a formal process control mechanism.

G$-$a$-$B took a sample of $50$ orders every hour $($with the business scaling up$,$ G$-$a$-$B was now delivering

many more orders per hour$)$ to check if the process was in control. Following industry norms, Anisha

used the $3-$sigma rule, i$.$e$.,$ the control limits were set at $\backslash$pm $3$

$$

$.$

One of the key drivers of external variability $($special cause variation$)$ affecting G$-$a$-$B$$s process is large

orders from customers, delaying G$-$a$-$B$$s delivery. It has been seen in the past that when this happens

the mean delivery time increases by $2\mathrm{.}5$ minutes but doesn$$t affect the variability $($SD$)$ of delivery times

significantly.

Remember, before the process improvement initiative efforts described in G$-$a$-$B $($C$),$ the average

delivery time and standard deviation of delivery time were $19\mathrm{.}32$ minutes and $7\mathrm{.}73$ minutes,

respectively.

Questions:

$(1)$ As Anisha sat down to compile all the benefits from the process improvements described in G$-$a$-$B

$($part C$),$ she pondered: $$Will higher sigma capability allow G$-$a$-$B to detect external variability $($special

cause variation$)$ faster than before?$$ Justify your answer.

$(2)$ How would your response to Q$1$ change if G$-$a$-$B decides to monitor processes using $2\mathrm{.}5$ sigma

control limits$.$ Explain the implications