Chapter $15$:

$1.)$ Do problem d$,$ e$,$ & f below $(2\mathrm{.}0$ points$).$ Data is in PS$2\_$F$23\_$Reyn$\_$Spooner.

Macy's sells Reyn Spooner Aloha Shirts and they are planning their $2023$ Christmas Reyn Spooner Collection. Macy's sales and marketing team wants to launch a pre$-$Christmas promotion to increase sales going into the $4^{th}$ quarter. Some management believe the promotion may be a waste of resources. This control chart will help evaluate if a sales promotion of this type is effective.

Keep in mind that the "non$-$conforming" items here are the # Reyn Spooner Aloha Shirts sold. Since the Totals vary, be sure to select the "Size varies" checkbox and set the range to the Total values.

Before the promotion $=$ days $1-30$ as you p$-$charted in $($a$).$ Look for any of the $4$ patterns $($i$.$e$.$ "rules"$)$ discussed. If it's in$-$control explain why by indicating that the data behaves as expected for Normally variation with $30$ data points i$.$e$."$We see no points outside the control limits which is expected since less that $1\%$ of the points are expected to fall outside, so for $30$ points we expect less than $0\mathrm{.}03$ or essentially $0$ points."

"Extend" here means use days $1-37.$ Keep in mind that "out$-$of$-$control" here is what we hope to see if the promotion is working! Just explain if you see an out$-$of$-$control pattern and if it indicates the expected effect from the promotion. Make sure you explain the pattern is "good" or "bad" for the process $($i$.$e$.$ bad $=$ less sales, good $=$ more sales$).$

$($d$)$ Explain why it is necessary to generate two $p-$charts and compare rather than just one $p-$chart for the $37$ days.

Think about this... what if the process on days $1-30($prior to the promotion$)$ was out$-$of$-$control? If it were, would you be able to conclude that an out$-$of$-$control pattern on days $1-37$ was caused by the promotion?

$($e$)$ Explain also why it would be insufficient to compare the chart with days $1-30$ with a chart for days $31-37.$

Remember that you are tiying to see the impact of a process change between days $1-30$ and days $31-37.$ Would you be able to see this easily and objectively if you compared the two charts as suggested? Explain why not and you will have answered this question!

$($f$)$ In this particular problem, is the process being out$-$of$-$control undesirable or indicates a problem that needs to be corrected? Explain!

Again, keep in mind the objective is to determine if the promotion had an impact. What would be a "good" impact $($i$.$e$.$ expected effect of the promotion$)$ vs$.$ a "bad" impact here? Now think about the out$-$of$-$control patterns. A "good" out$-$of$-$control pattern is one that indicates a good impact on the process. Is such a pattern possible here? If you have a good pattern, then was this impact what was expected or hoped for? If so$,$ does this mean you need to correct a problem?

PHStat Control Charts p charts