Process Quality Exercise

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.

Tom should use both the x-bar and R-charts since weight is a variable measure of quality. These charts must be used together.

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

Tom will need to take random samples of 10 bags each from the process. For each bag, he will measure the weight and record it. Then he will calculate the average weight of those 10 bags by averaging the 10 recorded weights. Finally, he will calculate the range of the weights by subtracting the smallest of the 10 weights from the largest of the 10 weights.

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

Answer should show the formulas for the x-bar and R-charts. In addition, the answer should explain that Tom will need to look up information in a table to estimate 3 standard deviations from the mean for the control limits.

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

Tom should continue taking samples at regular intervals to determine whether the process is still in control or not. If it is out of control, Tom will need to take action to fix the assignable cause of the variation.

"TOO MANY GREEN ONES" PROBLEM

1. Should Tom use the same or different type of chart(s) to analyze this problem?

Explain why.

Tom should use the p-chart. He must use a different chart since the quality characteristic being measured is an attribute. The background information suggests that he should not use a c-chart since he does not think it is reasonable to count each green gum drop as a defect.

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

Tom will need to gather random samples of 10 bags. For each bag, he will count the number of green gum drops. If the number is less than 2 or more than 4, then the bag is considered defective. Each plot on the p-chart will then show the proportion of the 10 bags that were defective. For example, if 2 out of the 10 bags have the wrong number of green ones, then the proportion defective is 0.20 (20%).

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

The answer should show the formulas for the center line and control limits for the p-chart.

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

Tom should continue taking samples at regular intervals to determine whether the process is still in control or not. If it is out of control, Tom will need to take action to fix the assignable cause of the variation.