The purpose of this exercise is to assess quality problems facing a production facility. The manager has hired you to help the production team. Your task is to determine what techniques to recommend and what data might be needed to address the quality issues.

You have been hired by m&m$\text{'}$s to address a quality problem. With Halloween just around the corner, production is in high gear for peanut m&m$\text{'}$s$.$ Most of the process is automated with the packages getting a mix of colors of candies. Each bag should contain $16$ ounces of candy; each candy is about one$-$half ounce. The mix in each bag should be approximately $20\%$ red, $20\%$ orange, $20\%$ yellow, $20\%$ blue, $10\%$ green, and $10\%$ brown.

Recently, the company has received customer complaints along two lines:

$1.$ Many are complaining that the bags do not appear full and believe that they are not getting a fair measure for the money they are paying, but no one has verified this.

$2.$ Several customers have complained about $$too many green ones$$ in the package. Some have even reported counting the total number of candies and the number of green ones in a package. No one has ever complained about $$too few green ones.$$

Diane, the plant manager has been given copies of the complaint letters and the assignment to $$fix the problem.$$ She has hired you to help her. She has decided his first step is to determine if there really is a problem with the process. Diane needs to implement lessons from Statistical Quality Control from Operations Management.

You need to figure out what information you need, how to analyze it$,$ and how to create a system to monitor the quality of the product to assure that these customer complaints do not arise in the future. At first, you were not sure whether to count the m&m$\text{'}$s$,$ weigh them, or use some other measure. After giving it more thought, you decided to take random samples of $10$ bags throughout the day from each of five production lines and use their weights to monitor a $$fair measure.$$

The problem of $$too many green ones$$ is a bit more difficult to formulate. Perhaps the green ones could be termed $$defects$,$ but then you would have to say that each bag should contain about $10\%$defects$.$ This wouldn't sound right in a report to the management. A better approach would be to say that since the bag should contain about $32$ m&m$\text{'}$s and $10\%$ of those should be green, any bag containing $2,3,$ or $4$ green ones would be a $$good$$ bag. Therefore, if a bag contained less than $2$ or more than $4$ green ones, the bag would be considered $$bad$$ or $$defective$$ with respect to the product specifications.

You must determine if they need a p$-$chart, an x$-$bar chart, an R$-$chart, or a c$-$chart. TOO LITTLE CANDY PROBLEM $-$ FAIR MEASURE

Data:

Bag Line $1$ Sample Line $2$ Sample Line $3$ Sample Line $4$ Sample Line $5$ Sample

$116\mathrm{.}0015\mathrm{.}5015\mathrm{.}7015\mathrm{.}1015\mathrm{.}20$

$215\mathrm{.}1014\mathrm{.}6014\mathrm{.}8014\mathrm{.}2014\mathrm{.}30$

$315\mathrm{.}5015\mathrm{.}0015\mathrm{.}2014\mathrm{.}6014\mathrm{.}70$

$415\mathrm{.}0014\mathrm{.}5014\mathrm{.}7014\mathrm{.}1014\mathrm{.}20$

$515\mathrm{.}5015\mathrm{.}0015\mathrm{.}2014\mathrm{.}6014\mathrm{.}70$

$615\mathrm{.}7015\mathrm{.}1015\mathrm{.}2015\mathrm{.}5016\mathrm{.}00$

$714\mathrm{.}9014\mathrm{.}3014\mathrm{.}4014\mathrm{.}7015\mathrm{.}20$

$815\mathrm{.}0014\mathrm{.}4014\mathrm{.}5014\mathrm{.}8015\mathrm{.}30$

$915\mathrm{.}1014\mathrm{.}5014\mathrm{.}6014\mathrm{.}9015\mathrm{.}40$

$1014\mathrm{.}7014\mathrm{.}1014\mathrm{.}2014\mathrm{.}5015\mathrm{.}00$

$1.$ What kind of chart $($or charts$)$ does the Team need to analyze this problem? Explain why you chose the chart or charts.

$2.$ Specifically, what information will the Team need to construct the chart$($s$)$ and how will the Team gather it$?$

$3.$ Explain the calculations the Team will need to make $$ including formulas and tables needed $$ to construct the chart$($s$).$

$4.$ After the Team has completed the chart$($s$),$ what should the team do over the next week or so$?$ TOO MANY GREEN ONES PROBLEM

Data:

Bag Line $1$ Sample Line $2$ Sample Line $3$ Sample Line $4$ Sample Line $5$ Sample

$16\mathrm{.}006\mathrm{.}005\mathrm{.}006\mathrm{.}004\mathrm{.}00$

$25\mathrm{.}005\mathrm{.}004\mathrm{.}004\mathrm{.}004\mathrm{.}00$

$33\mathrm{.}005\mathrm{.}004\mathrm{.}005\mathrm{.}005\mathrm{.}00$

$45\mathrm{.}004\mathrm{.}004\mathrm{.}002\mathrm{.}006\mathrm{.}00$

$55\mathrm{.}006\mathrm{.}006\mathrm{.}005\mathrm{.}002\mathrm{.}00$

$65\mathrm{.}006\mathrm{.}005\mathrm{.}003\mathrm{.}005\mathrm{.}00$

$74\mathrm{.}005\mathrm{.}004\mathrm{.}001\mathrm{.}002\mathrm{.}00$

$83\mathrm{.}004\mathrm{.}004\mathrm{.}005\mathrm{.}006\mathrm{.}00$

$94\mathrm{.}004\mathrm{.}003\mathrm{.}005\mathrm{.}005\mathrm{.}00$

$103\mathrm{.}003\mathrm{.}001\mathrm{.}005\mathrm{.}001\mathrm{.}00$

$1.$ Should the Team use the same or different type of chart$($s$)$ to analyze this problem? Explain why.

$2.$ Specifically, what information will the Team need to construct the chart$($s$)$ for this problem and how will they gather it$?$

$3.$ Explain the calculations the Team will need to make $$ including formulas and tables he will need $$ to construct the chart$($s$).$

$4.$ After the Team has completed the chart$($s$),$ what should the Team do over the next week or so$?$