Six Sigma Case Studies with Minitab®

61

5

Chi-Square Analysis to Verify

Quality of Candy Packets

This case study is about how chi-square analysis can be used in a Six Sigma

project to collect voice of the customer (VOC) data and then to verify if a

claim made about product quality is true.

Colorful Candy, Inc. makes colored chocolate candy and sells them in

packets that are claimed to contain 14% yellow candy, 13% red candy, 20%

orange candy, 24% blue candy, 16% green candy, and 13% purple candy. The

company wants to know whether the customers really care about the variety

of colors, and if so, whether the above claim of percentages is correct.

Section 5.1 gives a brief description of the dene phase. Section 5.2 explains

the measure phase. The analyze phase is illustrated in Section 5.3 with

detailed instructions for using Minitab

®

. Finally, the improve and control

phases are briey discussed in Section 5.4.

5.1 Define Phase

The company wants to ensure that customers are getting what they are

expecting regarding the percentages of different colors of candy in each

packet they are purchasing. However, before randomly selecting a packet

and testing it, the company executives decide to check whether customers

really care about the different colors.

5.2 Measure Phase

To gather the VOC data, a number of randomly selected customers in Boston,

Cleveland, New York City, San Francisco, and Chicago, are asked to rate on

a 1–7 scale, how important the variety of colors is to them, with 7 being

“extremely important” and 1 being “not important at all”. The collected data

are in the CHAPTER_5_1.MTW worksheet (the worksheet is available at the

62 Six Sigma Case Studies with Minitab

®

publisher’s website; the data from the worksheet are also provided in the

Appendix). A part of the worksheet is shown in Figure5.1.

5.3 Analyze Phase

A bar chart is plotted for the data collected. Figure5.2 shows how to select

“Bar Chart”. Doing so opens the dialog box shown in Figure5.3. Select “Values

from a table” from the drop-down menu, and select the “Stack” option under

“One column of values”. Click on “OK” and the dialog box shown in Figure5.4

opens. Select the “Observed” column for “Graph variables” and select “City”

and “Importance of Candy Color” for “Categorical variables for grouping”.

The bar chart shown in Figure5.5 is the result. Although it is clear from the

bar chart that customers in New York City seem to give a lot more importance

FIGURE 5.1

Data collected for importance given to candy color.

63Chi-Square Analysis to Verify Quality of Candy Packets

to candy color than those in the other cities, the company executives want to

perform a chi-square test of homogeneity to check whether the higher impor-

tance by customers in New York City is statistically signicant. Figure 5.6

shows how to select “Chi-Square”. Doing so will open the dialog box shown

in Figure5.7. Select “Importance of Candy Color” for “For rows” and “City”

for “For columns”. Select “Observed” for “Frequencies in” and check the box

for “Counts”. Click on “OK” and the output shown in Figure5.8 is the result.

The output shows how many customers were sampled in each of the cities and

how many customers gave what importance rating (1–7).

For expected values, click on “Chi-Square” in the dialog box shown in

Figure5.7, and the dialog box shown in Figure5.9 opens. Check the box for

“Expected cell counts” and click on “OK”. It takes you back to the dialog box

shown in Figure5.7. Click on “OK” and the output shown in Figure5.10 is

the result.

FIGURE 5.2

Selection of “Bar Chart.”

64 Six Sigma Case Studies with Minitab

®

FIGURE 5.3

Selection from options for bar chart.

FIGURE 5.4

Selection of variables for bar chart.

65Chi-Square Analysis to Verify Quality of Candy Packets

ChicagoSan

Francisco

New York

City

ClevelandBostonCity

1600

1400

1200

1000

800

600

400

200

0

Observed

1

2

3

4

5

6

7

Importance of

Candy Color

Chart of Observed

FIGURE 5.5

Bar chart.

FIGURE 5.6

Selection of chi-square test.