250 Part 3 • Implementing Quality

4.51 5.96 2.24 7.28 3.96 8.22 5.55 5.25 4.11 1.15

0.79 3.49 5.25 5.25 6.79 2.56 2.24 2.26 6.11 5.25

4.19 2.25 5.36 4.29 4.66 5.25 8.95 0.79 5.25 2.21

2,29 3,45 1.15 5.25 3.56 3.33 2.49 5.25 4.56 5.25

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value when developing a histogram because the histogram is often used to determine Develop a histogram of the sales. Solution: It is helpful to compute the mean, standard deviation, maximum value, and minimum whether the data are normally distributed. Following are these statistics from the previously given data:

Mean = 4.20 Maximum value = 8.95 Minimum value = .79 Difference = 8.16 Sum = 168 Using Formula (10.2)

k log 40/log 2 k 5.32 The number of classes is 6. Therefore, Classes = 6 Class width = 8.16/6 = 1.36 N 1.40 Classes = 0.76-2.15; 2.16-3.55; 3.56-4.95; 4.96-6.35; 6.36-7.75; 7.76-9.15

The histogram is displayed in Figure 10-9. Thus, the manager finds that sales occur in a skewed distribution with a mean of $4.20.

Scatter Diagrams The scatter diagram or scatter plot is used to examine the relationships between variables. These relationships are sometimes used to identify indicator variables in organizations. For example, in a hospital, the postoperative infection rate has been found to be associated wth,. many different factors, such as the sterile procedures used by the doctors and nurses, cleani .r. .) ness of the operating rooms, and sterile procedures for handling the utensils used in surge Therefore, the postoperative infection rate is an important variable for hospital quality measurement. It is quite easy to develop scatter plots using the charting facilities in spreadsheet packages_ such as Excel. Figure 10-10 shows a scatter plot of the relationship between conformance d and prevention and appraisal quality-related costs in a real firm. Note that the figure shows. the unexpected outcome of higher-quality costs with higher levels of conformance. Later anal): showed that this firm was trying to “inspect in” quality, meaning that it was throwing a lot o1in process work away as a result of more rigorous inspection. Use the following steps up a scatter plot: 1. Determine your x (independent) and y (dependent) variables. 2. Gather process data relating to the variables identified in step 1. when seta

I 00

a, g 0 80 60 40 20 • % • 600 se* . • 04,,, • • f •Ioit, • • • • • • 0. ••i• •

050 60 70 80 Conformance

FIGURE 10-10 Prevention Costs and Conformance

3. Plot the data on a two-dimensional plane. 4. Observe the plotted data to see whether there is a relationship between the variables. (Note that it is helpful to plot the data in Excel or another spreadsheet and to per-form a correlation test to determine whether the variables have a statistically significant relationship.)

Chapter 10 • The Tools of Quality 251

90 100

EXAMPLE 10-4

Scatter Diagrams

Problem: Healthy People, Inc., a company specializing in home health care solutions for U.S. consumers, was a growing company. The company wanted to study the relationship between absenteeism and the number of overtime hours worked by employees. Thirty employees were randomly selected, and numbers of overtime hours were graphed against numbers of days absent for the previous year (see Figure 10-11).

7 6 • Series 1 11M111 5 1111.111111.11111111 Q IIIIIIIIIIIIIPMIIM■■ 3 11111111.141111111111111111 2 4 2 11011011111111111111 z ■ 1 jiirill 111

■111 0 150 200 250 300 350 400 450 500 FIGURE 10-11 Scatter Plot of OvertimeoHoouvresrversus Days Absent

0 50 100

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