You just graduated from University of Kentucky and accepted a job with C&A Candy

Question

You just graduated from University of Kentucky and accepted a job with C&A Candy Company. One of C&A’s 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, C&A 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.

You have been given copies of the complaint letters and the assignment to "fix the problem."

You decide your first step is to determine if there really is a problem with the process. You have been trying to figure out what information you 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, you were not sure whether to count the gum drops, weigh them, or use some other measure

After giving it more thought, you have 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 you to formulate.

You thought about calling the green ones "defects" but then you 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, you 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.

Consider the fair measure problem, what kind of quality measure should be used in constructing the control chart(s)?

What kind of control chart(s) do you need to analyze the fair measure problem?

Consider the fair measure problem, how should the quality control data be collected?

What kind of control chart(s) do you need to analyze the too many green ones problem?

Consider the too many green ones problem, what kind of quality measure should be used in constructing the control chart(s)?

Explanation / Answer

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

Answer:- One 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 gumdrop as a defect. One 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%). One 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.

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