Exercise:

Tom Dooley just graduated from Arizona State and accepted a job with Meyerson Candy Company. One of their major products is gum drops that are packaged in an assortment of colors, each color being a different flavor. Most of the process is automated with machines producing the gum drops, mixing the different flavors, and packaging them in plastic bags. Each bag should contain 16 ounces of candy; each gum drop is about 1/2 ounce. The mix in each bag should be approximately 20% red (cherry), 20% orange, 20% white, 20% yellow (lemon) and 10% each of black (licorice), and green (lime).

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

1. Many are complaining that the bags do not appear full and they believe that they are not getting a fair measure for what 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 gum drops and the number of green ones in a package. No one has ever complained about too few green ones.

Tom has been given copies of the complaint letters and the assignment to "fix the problem." He decides his first step is to determine if there really is a problem with the process. To do that he will need to use the tools and ideas he learned in his Operations Management course.

Tom has been trying to figure out what information he needs, 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, he was not sure whether to count the gum drops, weigh them, or use some other measure. After giving it more thought, Tom has decided to take random samples of 10 bags throughout the day and use their weights to monitor "fair measure."

The problem of "too many green ones" is a bit more difficult for Tom to formulate. He thought about calling the green ones "defects" but then he would have to say that each bag should contain about 10% "defects" that wouldn't sound right in a report to management. A better approach, he thought, would be to say that since the bag should contain about 32 gum drops and 10% of those should be green, any bag containing 2 or 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.

Now, Tom has to determine if he needs a p-chart, an X-bar chart, an R-chart or what. He needs your help.

THE "FAIR MEASURE" PROBLEM

1. What kind of chart(s) does Tom need to analyze this problem? Explain why you chose the chart(s) he should use.

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

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

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