Deck 18: Statistical Applications in Quality Management

Question 1

TABLE 18-2
A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the percentage favoring the incumbent candidate is too erratic.
$\begin{array}{cc}\hline\text { Sample }&\text { Number Favoring}\\\text { (Day)}& \text { Incumbent Candidate }\\ \hline1 & 57 \\2 & 57 \\3 & 53 \\4 & 5 1 \\5 & 5 5 \\6 & 6 0 \\7 &5 6 \\8 & 5 9\\\hline\end{array}$



-Referring to Table 18-2, what is the numerical value of the upper control limit for the p chart?

A) 0.62
B) 0.89
C) 0.71
D) 0.92

Answer 1

0.71

Question 2

TABLE 18-3
A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day.
$$\begin{array} { l c c } \text { Day } & \bar { X } ( \text { in minutes } ) & \text { R } \\\hline 1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$$

-Referring to Table 18-3, suppose the analyst constructs an $\bar{X}$ chart to see if the production process is in-control. What is the center line for this chart?

A) 64.3
B) 57.1
C) 58.0
D) 59.5

Answer 2

58.0

Question 3

The principal focus of the control chart is the attempt to separate special or assignable causes of variation from common causes of variation. What cause of variation can be reduced only by changing the system?

A) common causes
B) total causes
C) special or assignable causes
D) none of the above

Answer 3

A

Question 4

Variation signaled by individual fluctuations or patterns in the data is called

A) explained variation.
B) the standard deviation.
C) special or assignable causes.
D) common or chance causes.

Question 5

TABLE 18-2
A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the percentage favoring the incumbent candidate is too erratic.
$\begin{array}{cc}\hline\text { Sample }&\text { Number Favoring}\\\text { (Day)}& \text { Incumbent Candidate }\\ \hline1 & 57 \\2 & 57 \\3 & 53 \\4 & 5 1 \\5 & 5 5 \\6 & 6 0 \\7 &5 6 \\8 & 5 9\\\hline\end{array}$


-Referring to Table 18-2, what is the numerical value of the lower control limit for the p chart?

A) 0.71
B) 0.41
C) 0.50
D) 0.37

Question 6

The Shewhart-Deming cycle plays an important role in which of the following Deming's 14 points for management?

A) Eliminate slogans, exhortation, and targets for the workforce.
B) Create constancy of purpose for improvement of product and services.
C) Adopt the new philosophy.
D) Break down barriers between staff areas.

Question 7

TABLE 18-1
A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every day. The owner decides to record the number of papers delivered on time for a 10-day period and construct a p chart to see whether the percentage is too erratic.
$\begin{array}{cc}&\text { Number of Papers }\\\text { Day } & \text { Delivered on Time } \\\hline1 & 46 & \\2 & 45 & \\3 & 46 & \\4 & 45 & \\5 & 43 & \\6 & 48 & \\7 & 46 & \\8 & 49 & \\9 & 48 & \\10 & 47 &\end{array}$


-Referring to Table 18-1, what is the numerical value of the center line for the p chart?

A) 0.885
B) 0.500
C) 0.911
D) 0.926

Question 8

Developing operational definitions for each critical-to-quality characteristic involves which part of the DMAIC process?

A) Define
B) Measure
C) Analyze
D) Improve
E) Control

Question 9

TABLE 18-3
A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day.
$$\begin{array} { l c r } \text { Day } & \bar { X } \text { (in minutes) } & \mathrm { R } \\\hline1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$$

-Referring to Table 18-3, suppose the analyst constructs an $\bar{X}$ chart to see if the production process is in-control. What is the lower control limit (LCL) for this chart?

A) 47.60
B) 57.15
C) 56.15
D) 58.05

Question 10

TABLE 18-1
A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every day. The owner decides to record the number of papers delivered on time for a 10-day period and construct a p chart to see whether the percentage is too erratic.
$\begin{array}{cc}&\text { Number of Papers }\\\text { Day } & \text { Delivered on Time } \\\hline1 & 46 & \\2 & 45 & \\3 & 46 & \\4 & 45 & \\5 & 43 & \\6 & 48 & \\7 & 46 & \\8 & 49 & \\9 & 48 & \\10 & 47 &\end{array}$

-Referring to Table 18-1, which expression best characterizes the p chart?

A) cycles
B) in-control
C) individual outliers
D) increasing trend

Question 11

TABLE 18-3
A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day.
$$\begin{array} { l c c } \text { Day } & \bar { X } \text { (in minutes) } & \text { R } \\\hline 1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$$

-Referring to Table 18-3, suppose the analyst constructs an $\bar{X}$ chart to see if the production process is in-control. What is the upper control limit (UCL) for this chart?

A) 58.75
B) 59.85
C) 62.15
D) 60.95

Question 12

Determining the root causes of why defects can occur along with the variables in the process that cause these defects to occur involves which part of the DMAIC process?

A) Define
B) Measure
C) Analyze
D) Improve
E) Control

Question 13

Which of the following situations suggests a process that appears to be operating in a state of statistical control?

A) a control chart in which no points fall outside either the upper control limit or the lower control limit and no patterns are present
B) a control chart in which several points fall outside the upper control limit
C) a control chart with a series of consecutive points that are above the center line and a series of consecutive points that are below the center line
D) all of the above

Question 14

Which of the following situations suggests a process that appears to be operating out of statistical control?

A) a control chart with a series of consecutive points that are above the center line and a series of consecutive points that are below the center line
B) a control chart in which several points fall outside the upper control limit
C) a control chart in which points fall outside the lower control limit
D) all of the above

Question 15

Which famous statistician developed the 14 Points of Quality?

A) Deming
B) Taguchi
C) Chebyshev
D) Shewhart

Question 16

TABLE 18-4
A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.
$\begin{array}{lll}\text { Hour } &\bar{X} &R\\\hline & & \\1 & 18.4 & 25 \\2 & 16.9 & 27 \\3 & 23.0 & 30 \\4 & 21.2 & 23 \\5 & 21.0 & 24 \\6 & 24.0 & 25 \\7 & 19.3 & 12 \\8 & 15.8 & 14 \\9 & 20.0 & 13 \\10 & 23.0 & 11\end{array}$
She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively.


-Referring to Table 18-4, suppose the supervisor constructs an $\bar{X}$ chart to see if the process is in-control. What is the center line of the chart?

A) 21.00
B) 20.00
C) 24.26
D) 20.26

Question 17

TABLE 18-3
A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day.
$$\begin{array} { l c c } \text { Day } & \bar { X } \text { (in minutes) } & R \\\hline 1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$$

-Referring to Table 18-3, suppose the sample mean and range data were based on 11 observations per day instead of 10. How would this change affect the lower and upper control limits of the R chart?

A) LCL would remain the same; UCL would decrease.
B) LCL would increase; UCL would decrease.
C) Both LCL and UCL would remain the same.
D) LCL would decrease; UCL would increase.

Question 18

TABLE 18-1
A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every day. The owner decides to record the number of papers delivered on time for a 10-day period and construct a p chart to see whether the percentage is too erratic.
$\begin{array}{cc}&\text { Number of Papers }\\\text { Day } & \text { Delivered on Time } \\\hline1 & 46 & \\2 & 45 & \\3 & 46 & \\4 & 45 & \\5 & 43 & \\6 & 48 & \\7 & 46 & \\8 & 49 & \\9 & 48 & \\10 & 47 &\end{array}$


-Referring to Table 18-1, what is the numerical value of the lower control limit for the p chart?

A) 0.920
B) 0.815
C) 0.798
D) 0.911

Question 19

Which of the following is not part of the DMAIC process in Six Sigma management?

A) Do
B) Define
C) Analyze
D) Control

Question 20

Which of the following is not one of Deming's 14 points?

A) Create constancy of purpose for improvement of product or service.
B) Adopt and institute leadership.
C) Drive out fear.
D) Belief in mass inspection.

Question 21

One of the morals of the red bead experiment is

A) it is the system that primarily determines performance.
B) only management can change the system.
C) variation is part of the process.
D) all of the above

Question 22

TABLE 18-4
A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.
$$\begin{array} { l l l l } \text { Hour } & \bar { X } & \text { R } \\\hline 1 & 18.4 & 25 \\2 & 16.9 & 27 & \\3 & 23.0 & 30 & \\4 & 21.2 & 23 & \\5 & 21.0 & 24 & \\6 & 24.0 & 25 & \\7 & 19.3 & 12 \\8 & 15.8 & 14 & \\9 & 20.0 & 13 & \\10 & 23.0 & 11 &\end{array}$$ She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively.

-Referring to Table 18-4, suppose the sample mean and range data were based on 6 observations per hour instead of 5. How would this change affect the lower and upper control limits of an R chart?

A) LCL would decrease; UCL would increase.
B) LCL would remain the same; UCL would decrease.
C) LCL would increase; UCL would decrease.
D) Both LCL and UCL would remain the same.

Question 23

Variation due to the inherent variability in a system of operation is called

A) special or assignable causes.
B) the standard deviation.
C) common or chance causes.
D) explained variation.

Question 24

TABLE 18-1
A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every day. The owner decides to record the number of papers delivered on time for a 10-day period and construct a p chart to see whether the percentage is too erratic.
$\begin{array}{cc}&\text { Number of Papers }\\\text { Day } & \text { Delivered on Time } \\1 & 46 & \\2 & 45 & \\3 & 46 & \\4 & 45 & \\5 & 43 & \\6 & 48 & \\7 & 46 & \\8 & 49 & \\9 & 48 & \\10 & 47 &\end{array}$


-Referring to Table 18-1, what is the numerical value of the upper control limit for the p chart?

A) 0.926
B) 0.961
C) 1.000
D) 0.979

Question 25

TABLE 18-3
A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day.
$$\begin{array} {ccc} \text { Day } & \bar { X } \text { (in minutes) } & R \\\hline1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$$

-Referring to Table 18-3, suppose the analyst constructs an R chart to see if the variability in production times is in-control. The R chart is characterized by which of the following?

A) jump in the level around which the observations vary
B) hugging the center line
C) hugging the control limits
D) increasing trend

Question 26

TABLE 18-2
A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the percentage favoring the incumbent candidate is too erratic.
$\begin{array}{cc}\hline\text { Sample }&\text { Number Favoring}\\\text { (Day)}& \text { Incumbent Candidate }\\ \hline1 & 57 \\2 & 57 \\3 & 53 \\4 & 5 1 \\5 & 5 5 \\6 & 6 0 \\7 &5 6 \\8 & 5 9\\\hline\end{array}$



-Referring to Table 18-2, what is the numerical value of the center line for the p chart?

A) 0.63
B) 0.53
C) 0.66
D) 0.56

Question 27

TABLE 18-4
A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.
$$\begin{array} { l l l l } \text { Hour } & \bar { X } & \text { R } \\\hline 1 & 18.4 & 25 \\2 & 16.9 & 27 & \\3 & 23.0 & 30 & \\4 & 21.2 & 23 & \\5 & 21.0 & 24 & \\6 & 24.0 & 25 & \\7 & 19.3 & 12 \\8 & 15.8 & 14 & \\9 & 20.0 & 13 & \\10 & 23.0 & 11 &\end{array}$$ She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively.

-Referring to Table 18-4, suppose the supervisor constructs an R chart to see if the variability in collection times is in-control. What is the center line of this R chart?

A) 24.00
B) 20.00
C) 20.56
D) 20.40

Question 28

TABLE 18-3
A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day.
$$\begin{array} { l c c } \text { Day } & \bar { X } \text { (in minutes) } & R \\\hline 1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$$

-Referring to Table 18-3, suppose the analyst constructs an R chart to see if the variability in production times is in-control. What is the center line of this R chart?

A) 6.0
B) 6.9
C) 4.8
D) 7.1

Question 29

TABLE 18-4
A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.
$$\begin{array} { l l l l } \text { Hour } & \bar { X } & \text { R } \\\hline 1 & 18.4 & 25 \\2 & 16.9 & 27 & \\3 & 23.0 & 30 & \\4 & 21.2 & 23 & \\5 & 21.0 & 24 & \\6 & 24.0 & 25 & \\7 & 19.3 & 12 \\8 & 15.8 & 14 & \\9 & 20.0 & 13 & \\10 & 23.0 & 11 &\end{array}$$ She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively.

-Referring to Table 18-4, suppose the supervisor constructs an $\bar{ X}$ chart to see if the process is in-control. Which expression best describes this chart?

A) cycles
B) decreasing trend
C) hugging the center line
D) increasing trend

Question 30

Referring to Table 18-3, suppose the analyst constructs an R chart to see if the variability in production times is in-control. What is the lower control limit for this R chart?

A) 1.34
B) 3.37
C) 4.84
D) 2.98

Question 31

A process is said to be out of control if

A) a point falls above the upper or below the lower control lines.
B) a run of 8 of more points is observed.
C) either of the above
D) none of the above

Question 32

Once the control limits are set for a control chart, one attempts to

A) discern patterns that might exist in values over time.
B) determine whether any points fall outside the control limits.
C) both of the above
D) none of the above

Question 33

Which of the following is not one of Deming's 14 points?

A) Award business on the basis of price tag alone.
B) Create constancy of purpose for improvement of product or service.
C) Break down barriers between staff areas.
D) Drive out fear.

Question 34

Which of the following best measures the ability of a process to consistently meet specified customer-driven requirement?

A) lower control limit
B) upper control limit
C) specification limits
D) process capability

Question 35

TABLE 18-3
A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day.
$\begin{array}{ccc}\text { Day } &\bar{X} &\text { (in minutes) }\\\hline1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$

-Referring to Table 18-3, suppose the analyst constructs an X chart to see if the production process is in-control. Which expression best describes this chart?

A) individual outliers
B) in-control
C) hugging the center line
D) increasing trend

Question 36

TABLE 18-2
A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the percentage favoring the incumbent candidate is too erratic.
$\begin{array}{cc}\hline\text { Sample }&\text { Number Favoring}\\\text { (Day)}& \text { Incumbent Candidate }\\ \hline1 & 57 \\2 & 57 \\3 & 53 \\4 & 51 \\5 & 55 \\6 & 60 \\7 & 56 \\8 & 59\\\hline\end{array}$




-Referring to Table 18-2, which expression best characterizes the p chart?

A) individual outliers
B) cycles
C) hugging the center line
D) hugging the control line

Question 37

TABLE 18-4
A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.
$$\begin{array} { l l l l } \text { Hour } & \bar { X } & \text { R } \\\hline 1 & 18.4 & 25 \\2 & 16.9 & 27 & \\3 & 23.0 & 30 & \\4 & 21.2 & 23 & \\5 & 21.0 & 24 & \\6 & 24.0 & 25 & \\7 & 19.3 & 12 \\8 & 15.8 & 14 & \\9 & 20.0 & 13 & \\10 & 23.0 & 11 &\end{array}$$ She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively.

-Referring to Table 18-4, suppose the supervisor constructs an R chart to see if the variability in collection times is in-control. What are the lower and upper control limits for this R chart?

A) 0, 42.28
B) - 2.33, 43.13
C) 0, 43.13
D) - 2.28, 42.28

Question 38

TABLE 18-4
A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.

$\begin{array} { l c c } \text {Hour}&\bar { X } & R \\ \hline1 & 18.4 & 25 \\ 2 & 16.9 & 27 \\ 3 & 23.0 & 30 \\ 4 & 21.2 & 23 \\ 5 & 21.0 & 24 \\ 6 & 24.0 & 25 \\ 7 & 19.3 & 12 \\ 8 & 15.8 & 14 \\ 9 & 20.0 & 13 \\ 10 & 23.0 & 11 \end{array}$
She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively.


-Referring to Table 18-4, suppose the supervisor constructs an X chart to see if the process is in-control. What are the lower and upper control limits of this chart?

A) 8.49, 32.03
B) 10.00, 30.00
C) 5.39, 35.13
D) 4.96, 35.56

Question 39

TABLE 18-3
A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day.
$$\begin{array}{ccc}\text { Day }& \bar { X } \text { (in minutes) } & R\\\hline1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$$

-Referring to Table 18-3, suppose the analyst constructs an R chart to see if the variability in production times is in-control. What is the upper control limit for this R chart?

A) 6.34
B) 10.66
C) 9.37
D) 7.98

Question 40

Which of the following is not part of the Shewhart-Deming cycle?

A) React
B) Do
C) Plan
D) Act

Question 41

TABLE 18-6
The maker of a packaged candy wants to evaluate the quality of her production process. On each of 16 consecutive days, she samples 600 bags of candy and determines the number in each day's sample that she considers to be of poor quality. The data that she developed follows.
$\begin{array}{lcl}\text { Day}& \text {Number Poor } & \text { Proportion Poor } \\1 & 33 & 0.0550000 \\2 & 29 & 0.0483333 \\3 & 31 & 0.0516667 \\4 & 32 & 0.0533333 \\5 & 43 & 0.0716667 \\6 & 45 & 0.0750000 \\7 & 46 & 0.0766667 \\8 & 48 & 0.0500000 \\9 & 48 & 0.0500000 \\10 & 46 & 0.0766667 \\11 & 28 & 0.0466667 \\12 & 32 & 0.0533333 \\13 & 28 & 0.0466667 \\14 & 32 & 0.0533333 \\15 & 31 & 0.0516667 \\16 & 24 & 0.0400000\end{array}$



-Referring to Table 18-6, construct a p control chart for these data.

Question 42

Maintaining the gains that have been made with a revised process in the long term by avoiding potential problems that can occur when a process is changed involves which part of the DMAIC process?

A) Define
B) Measure
C) Analyze
D) Improve
E) Control

Question 43

TABLE 18-8
Recently, a university switched to a new type of computer-based registration. The registrar is concerned with the amount of time students are spending on the computer registering under the new system. She decides to randomly select 8 students on each of the 12 days of the registration and determine the time each spends on the computer registering. The range, mean, and standard deviation of the times required to register are in the table that follows.
$$\begin{array} { c c l l } \text { Day } & \text { Range } & \text { Mean } & \text { Std.Dev. } \\1 & 10 & 5.250 & 3.4949 \\2 & 31 & 15.250 & 10.3060 \\3 & 13 & 20.375 & 4.9262 \\4 & 21 & 22.875 & 8.3911 \\5 & 35 & 8.500 & 11.3767 \\6 & 18 & 7.875 & 6.9372 \\7 & 25 & 11.250 & 8.5815 \\8 & 30 & 7.875 & 9.5235 \\9 & 17 & 10.250 & 6.3640 \\10 & 22 & 9.500 & 7.8740 \\11 & 27 & 7.875 & 8.7086 \\12 & 26 & 12.875 & 9.3723\end{array}$$

-Referring to Table 18-8, an R chart is to be constructed for the time required to register. The center line of this R chart is located at _____.

Question 44

18-7
A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes samples of size 5 from each day's output and counts the number of blemishes on each silicone sheet. The results from 20 days of such evaluations are presented below.
Sheet
$\begin{array}{llllllllll}\text { Day } & 1 & 2 & 3 & 4 & 5 & \text { Mean } & \text { Range } \\1 & 8 & 10 & 14 & 6 & 5 & 8.6 & 9 \\2 & 8 & 13 & 6 & 6 & 10 & 8.6 & 7 \\3 & 10 & 12 & 7 & 7 & 9 & 9.0 & 5 \\4 & 5 & 9 & 12 & 7 & 10 & 8.6 & 7 \\5 & 8 & 3 & 8 & 9 & 10 & 7.6 & 7 \\6 & 9 & 7 & 9 & 6 & 9 & 8.0 & 3 \\7 & 10 & 10 & 5 & 7 & 6 & 7.6 & 5 \\8 & 10 & 9 & 10 & 6 & 5 & 8.0 & 5 \\9 & 6 & 10 & 6 & 9 & 9 & 8.0 & 4 \\10 & 6 & 9 & 8 & 6 & 8 & 7.4 & 3 \\11 & 8 & 5 & 6 & 10 & 10 & 7.8 & 5 \\12 & 6 & 4 & 7 & 7 & 12 & 7.2 & 8 \\13 & 7 & 5 & 7 & 6 & 9 & 6.8 & 4 \\14 & 5 & 8 & 8 & 7 & 6 & 6.8 & 3 \\15 & 7 & 12 & 10 & 6 & 10 & 9.0 & 6 \\16 & 7 & 11 & 4 & 7 & 8 & 7.4 & 7 \\17 & 8 & 4 & 5 & 4 & 7 & 5.6 & 4 \\18 & 11 & 4 & 11 & 11 & 10 & 9.4 & 7 \\19 & 6 & 10 & 6 & 10 & 10 & 8.4 & 4 \\20 & 6 & 12 & 12 & 6 & 8 & 8.8 & 6\end{array}$

She also decides that the upper specification limit is 10 blemishes.

-Referring to Table 18-7, an R chart is to be constructed for the number of blemishes. The center line of this R chart is located at_____ .

Question 45

TABLE 18-9
The manufacturer of cat food constructed control charts and analyzed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 pounds. The table below provides the range and mean of the weights of five cans tested every fifteen minutes during a day's production.

$\begin{array}{cllccc}\hline \text { Number } & \text { XBar } & \text { Range } & \text { Number } & \text { XBar } & \text { Range } \\\hline 1 & 3.05072 & 0.0215 & 16 & 3.04646 & 0.073 \\2 & 3.01228 & 0.087 & 17 & 3.03868 & 0.0696 \\3 & 3.03558 & 0.0851 & 18 & 3.03338 & 0.0329 \\4 & 3.01014 & 0.0674 & 19 & 3.03322 & 0.0455 \\5 & 3.00858 & 0.0983 & 20 & 3.05078 & 0.0215 \\6 & 3.02704 & 0.0527 & 21 & 3.04808 & 0.0396 \\7 & 3.04268 & 0.0508 & 22 & 3.05348 & 0.0581 \\8 & 3.01052 & 0.0791 & 23 & 3.05516 & 0.0682 \\9 & 3.03464 & 0.0663 & 24 & 3.03426 & 0.0325 \\10 & 3.02034 & 0.0538 & 25 & 3.0516 & 0.0641 \\11 & 3.03764 & 0.0584 & 26 & 3.05562 & 0.0809 \\12 & 3.0409 & 0.0434 & 27 & 3.04402 & 0.0374 \\13 & 3.0519 & 0.0762 & 28 & 3.06458 & 0.0284 \\14 & 3.03994 & 0.0833 & 29 & 3.0544 & 0.0738 \\15 & 3.03788 & 0.0601 & & & \\\hline\end{array}$


-Referring to Table 18-9, an R chart is to be constructed for the weight. The upper control limit for this data set is _____.

Question 46

TABLE 18-4
A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.
$$\begin{array} { l l l l } \text { Hour } & \bar { X } & \text { R } \\\hline 1 & 18.4 & 25 \\2 & 16.9 & 27 & \\3 & 23.0 & 30 & \\4 & 21.2 & 23 & \\5 & 21.0 & 24 & \\6 & 24.0 & 25 & \\7 & 19.3 & 12 \\8 & 15.8 & 14 & \\9 & 20.0 & 13 & \\10 & 23.0 & 11 &\end{array}$$ She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively.

-Referring to Table 18-4, suppose the supervisor constructs an R chart to see if the variability in collection times is in-control. This R chart is characterized by which of the following?

A) hugging the control limits
B) cycles
C) jump in the level around which the observations vary
D) increasing trend

Question 47

TABLE 18-8
Recently, a university switched to a new type of computer-based registration. The registrar is concerned with the amount of time students are spending on the computer registering under the new system. She decides to randomly select 8 students on each of the 12 days of the registration and determine the time each spends on the computer registering. The range, mean, and standard deviation of the times required to register are in the table that follows.
$$\begin{array} { c c l l } \text { Day } & \text { Range } & \text { Mean } & \text { Std.Dev. } \\1 & 10 & 5.250 & 3.4949 \\2 & 31 & 15.250 & 10.3060 \\3 & 13 & 20.375 & 4.9262 \\4 & 21 & 22.875 & 8.3911 \\5 & 35 & 8.500 & 11.3767 \\6 & 18 & 7.875 & 6.9372 \\7 & 25 & 11.250 & 8.5815 \\8 & 30 & 7.875 & 9.5235 \\9 & 17 & 10.250 & 6.3640 \\10 & 22 & 9.500 & 7.8740 \\11 & 27 & 7.875 & 8.7086 \\12 & 26 & 12.875 & 9.3723\end{array}$$

-Referring to Table 18-8, an R chart is to be constructed for the time required to register. The upper control limit for this data set is _____.

Question 48

$$\text { TABLE 18-9 }$$
The manufacturer of cat food constructed control charts and analyzed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 pounds. The table below provides the range and mean of the weights of five cans tested every fifteen minutes during a day's production.

$\begin{array}{cllccc}\hline \text { Number } & \text { XBar } & \text { Range } & \text { Number } & \text { XBar } & \text { Range } \\\hline 1 & 3.05072 & 0.0215 & 16 & 3.04646 & 0.073 \\2 & 3.01228 & 0.087 & 17 & 3.03868 & 0.0696 \\3 & 3.03558 & 0.0851 & 18 & 3.03338 & 0.0329 \\4 & 3.01014 & 0.0674 & 19 & 3.03322 & 0.0455 \\5 & 3.00858 & 0.0983 & 20 & 3.05078 & 0.0215 \\6 & 3.02704 & 0.0527 & 21 & 3.04808 & 0.0396 \\7 & 3.04268 & 0.0508 & 22 & 3.05348 & 0.0581 \\8 & 3.01052 & 0.0791 & 23 & 3.05516 & 0.0682 \\9 & 3.03464 & 0.0663 & 24 & 3.03426 & 0.0325 \\10 & 3.02034 & 0.0538 & 25 & 3.0516 & 0.0641 \\11 & 3.03764 & 0.0584 & 26 & 3.05562 & 0.0809 \\12 & 3.0409 & 0.0434 & 27 & 3.04402 & 0.0374 \\13 & 3.0519 & 0.0762 & 28 & 3.06458 & 0.0284 \\14 & 3.03994 & 0.0833 & 29 & 3.0544 & 0.0738 \\15 & 3.03788 & 0.0601 & & & \\\hline\end{array}$



-Referring to Table 18-9, construct an X chart for the weight.

Question 49

TABLE 18-8
Recently, a university switched to a new type of computer-based registration. The registrar is concerned with the amount of time students are spending on the computer registering under the new system. She decides to randomly select 8 students on each of the 12 days of the registration and determine the time each spends on the computer registering. The range, mean, and standard deviation of the times required to register are in the table that follows.
$$\begin{array} { c c l l } \text { Day } & \text { Range } & \text { Mean } & \text { Std.Dev. } \\1 & 10 & 5.250 & 3.4949 \\2 & 31 & 15.250 & 10.3060 \\3 & 13 & 20.375 & 4.9262 \\4 & 21 & 22.875 & 8.3911 \\5 & 35 & 8.500 & 11.3767 \\6 & 18 & 7.875 & 6.9372 \\7 & 25 & 11.250 & 8.5815 \\8 & 30 & 7.875 & 9.5235 \\9 & 17 & 10.250 & 6.3640 \\10 & 22 & 9.500 & 7.8740 \\11 & 27 & 7.875 & 8.7086 \\12 & 26 & 12.875 & 9.3723\end{array}$$

-Referring to Table 18-8, an $\bar{X }$ chart is to be used for the time required to register. One way to obtain the control limits is to take the grand mean and add and subtract the product of A2 times the average of the sample ranges. For this data set, the value of A2 is ______.

Question 50

TABLE 18-9
The manufacturer of cat food constructed control charts and analyzed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 pounds. The table below provides the range and mean of the weights of five cans tested every fifteen minutes during a day's production.
$\begin{array}{cllccc}\hline \text { Number } & \text { XBar } & \text { Range } & \text { Number } & \text { XBar } & \text { Range } \\\hline 1 & 3.05072 & 0.0215 & 16 & 3.04646 & 0.073 \\2 & 3.01228 & 0.087 & 17 & 3.03868 & 0.0696 \\3 & 3.03558 & 0.0851 & 18 & 3.03338 & 0.0329 \\4 & 3.01014 & 0.0674 & 19 & 3.03322 & 0.0455 \\5 & 3.00858 & 0.0983 & 20 & 3.05078 & 0.0215 \\6 & 3.02704 & 0.0527 & 21 & 3.04808 & 0.0396 \\7 & 3.04268 & 0.0508 & 22 & 3.05348 & 0.0581 \\8 & 3.01052 & 0.0791 & 23 & 3.05516 & 0.0682 \\9 & 3.03464 & 0.0663 & 24 & 3.03426 & 0.0325 \\10 & 3.02034 & 0.0538 & 25 & 3.0516 & 0.0641 \\11 & 3.03764 & 0.0584 & 26 & 3.05562 & 0.0809 \\12 & 3.0409 & 0.0434 & 27 & 3.04402 & 0.0374 \\13 & 3.0519 & 0.0762 & 28 & 3.06458 & 0.0284 \\14 & 3.03994 & 0.0833 & 29 & 3.0544 & 0.0738 \\15 & 3.03788 & 0.0601 & & & \\\hline\end{array}$


-Referring to Table 18-9, construct an R chart for the time required to register.

Question 51

TABLE 18-5
A manufacturer of computer disks took samples of 240 disks on 15 consecutive days. The number of disks with bad sectors was determined for each of these samples. The results are in the table that follows.
$$\begin{array} { l l l } \text { Day } & \text { Bad } & \% \text { Bad } \\\hline 1 & 9 & 0037500 \\2 & 7 & 0.029167 \\3 & 4 & 0.016667 \\4 & 6 & 0.025000 \\5 & 8 & 0.033333 \\6 & 3 & 0.012500 \\7 & 6 & 0.025000 \\8 & 10 & 0.041667 \\9 & 16 & 0.066667 \\10 & 24 & 0.100000 \\11 & 15 & 0.062500 \\12 & 9 & 0.037500 \\13 & 4 & 0.016667 \\14 & 8 & 0.033333 \\15 & 6 & 0.025000\end{array}$$

-Referring to Table 18-5, a p control chart is to be made for these data. The estimate of the standard error of the proportion of disks with bad sectors is___________ .

Question 52

TABLE 18-5
A manufacturer of computer disks took samples of 240 disks on 15 consecutive days. The number of disks with bad sectors was determined for each of these samples. The results are in the table that follows.
$$\begin{array} { l l l } \text { Day } & \text { Bad } & \% \text { Bad } \\\hline 1 & 9 & 0037500 \\2 & 7 & 0.029167 \\3 & 4 & 0.016667 \\4 & 6 & 0.025000 \\5 & 8 & 0.033333 \\6 & 3 & 0.012500 \\7 & 6 & 0.025000 \\8 & 10 & 0.041667 \\9 & 16 & 0.066667 \\10 & 24 & 0.100000 \\11 & 15 & 0.062500 \\12 & 9 & 0.037500 \\13 & 4 & 0.016667 \\14 & 8 & 0.033333 \\15 & 6 & 0.025000\end{array}$$

-Referring to Table 18-5, a p control chart is to be made for these data. The center line of the control chart is _____ .

Question 53

The control chart

A) captures the natural variability in the system.
B) can be used for categorical, discrete, or continuous variables.
C) focuses on the time dimension of a system.
D) all of the above

Question 54

TABLE 18-7
A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes samples of size 5 from each day's output and counts the number of blemishes on each silicone sheet. The results from 20 days of such evaluations are presented below.
Sheet
$\begin{array}{llllllllll}\text { Day } & 1 & 2 & 3 & 4 & 5 & \text { Mean } & \text { Range } \\\hline 1 & 8 & 10 & 14 & 6 & 5 & 8.6 & 9 \\2 & 8 & 13 & 6 & 6 & 10 & 8.6 & 7 \\3 & 10 & 12 & 7 & 7 & 9 & 9.0 & 5 \\4 & 5 & 9 & 12 & 7 & 10 & 8.6 & 7 \\5 & 8 & 3 & 8 & 9 & 10 & 7.6 & 7 \\6 & 9 & 7 & 9 & 6 & 9 & 8.0 & 3 \\7 & 10 & 10 & 5 & 7 & 6 & 7.6 & 5 \\8 & 10 & 9 & 10 & 6 & 5 & 8.0 & 5 \\9 & 6 & 10 & 6 & 9 & 9 & 8.0 & 4 \\10 & 6 & 9 & 8 & 6 & 8 & 7.4 & 3 \\11 & 8 & 5 & 6 & 10 & 10 & 7.8 & 5 \\12 & 6 & 4 & 7 & 7 & 12 & 7.2 & 8 \\13 & 7 & 5 & 7 & 6 & 9 & 6.8 & 4 \\14 & 5 & 8 & 8 & 7 & 6 & 6.8 & 3 \\15 & 7 & 12 & 10 & 6 & 10 & 9.0 & 6 \\16 & 7 & 11 & 4 & 7 & 8 & 7.4 & 7 \\17 & 8 & 4 & 5 & 4 & 7 & 5.6 & 4 \\18 & 11 & 4 & 11 & 11 & 10 & 9.4 & 7 \\19 & 6 & 10 & 6 & 10 & 10 & 8.4 & 4 \\20 & 6 & 12 & 12 & 6 & 8 & 8.8 & 6\end{array}$

She also decides that the upper specification limit is 10 blemishes.

-Referring to Table 18-7, what is the value of the CPU index?

Question 55

TABLE 18-9
The manufacturer of cat food constructed control charts and analyzed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 pounds. The table below provides the range and mean of the weights of five cans tested every fifteen minutes during a day's production.
$\begin{array}{cllccc}\hline \text { Number } & \text { XBar } & \text { Range } & \text { Number } & \text { XBar } & \text { Range } \\\hline 1 & 3.05072 & 0.0215 & 16 & 3.04646 & 0.073 \\2 & 3.01228 & 0.087 & 17 & 3.03868 & 0.0696 \\3 & 3.03558 & 0.0851 & 18 & 3.03338 & 0.0329 \\4 & 3.01014 & 0.0674 & 19 & 3.03322 & 0.0455 \\5 & 3.00858 & 0.0983 & 20 & 3.05078 & 0.0215 \\6 & 3.02704 & 0.0527 & 21 & 3.04808 & 0.0396 \\7 & 3.04268 & 0.0508 & 22 & 3.05348 & 0.0581 \\8 & 3.01052 & 0.0791 & 23 & 3.05516 & 0.0682 \\9 & 3.03464 & 0.0663 & 24 & 3.03426 & 0.0325 \\10 & 3.02034 & 0.0538 & 25 & 3.0516 & 0.0641 \\11 & 3.03764 & 0.0584 & 26 & 3.05562 & 0.0809 \\12 & 3.0409 & 0.0434 & 27 & 3.04402 & 0.0374 \\13 & 3.0519 & 0.0762 & 28 & 3.06458 & 0.0284 \\14 & 3.03994 & 0.0833 & 29 & 3.0544 & 0.0738 \\15 & 3.03788 & 0.0601 & & & \\\hline\end{array}$




-Referring to Table 18-9, an R chart is to be constructed for the weight. The lower control limit for this data set is _____.

Question 56

TABLE 18-4
A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.
$$\begin{array} { l l l l } \text { Hour } & \bar { X } & \text { R } \\\hline 1 & 18.4 & 25 \\2 & 16.9 & 27 & \\3 & 23.0 & 30 & \\4 & 21.2 & 23 & \\5 & 21.0 & 24 & \\6 & 24.0 & 25 & \\7 & 19.3 & 12 \\8 & 15.8 & 14 & \\9 & 20.0 & 13 & \\10 & 23.0 & 11 &\end{array}$$ She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively.

-Referring to Table 18-4, what percentage of the time it takes workers to complete an important production task will fall inside the specification limits?

Question 57

TABLE 18-6
The maker of a packaged candy wants to evaluate the quality of her production process. On each of 16 consecutive days, she samples 600 bags of candy and determines the number in each day's sample that she considers to be of poor quality. The data that she developed follows.
$\begin{array}{lcl}&\text {Number}&\text { Proportion }\\\text { Day}& \text { Poor } & \text { Poor } \\\hline1 & 33 & 0.0550000 \\2 & 29 & 0.0483333 \\3 & 31 & 0.0516667 \\4 & 32 & 0.0533333 \\5 & 43 & 0.0716667 \\6 & 45 & 0.0750000 \\7 & 46 & 0.0766667 \\8 & 48 & 0.0500000 \\9 & 48 & 0.0500000 \\10 & 46 & 0.0766667 \\11 & 28 & 0.0466667 \\12 & 32 & 0.0533333 \\13 & 28 & 0.0466667 \\14 & 32 & 0.0533333 \\15 & 31 & 0.0516667 \\16 & 24 & 0.0400000\end{array}$


-Referring to Table 18-6, a p control chart is to be constructed for these data. The center line for the chart should be located at _____.

Question 58

TABLE 18-8
Recently, a university switched to a new type of computer-based registration. The registrar is concerned with the amount of time students are spending on the computer registering under the new system. She decides to randomly select 8 students on each of the 12 days of the registration and determine the time each spends on the computer registering. The range, mean, and standard deviation of the times required to register are in the table that follows.
$$\begin{array} { c c l l } \text { Day } & \text { Range } & \text { Mean } & \text { Std.Dev. } \\1 & 10 & 5.250 & 3.4949 \\2 & 31 & 15.250 & 10.3060 \\3 & 13 & 20.375 & 4.9262 \\4 & 21 & 22.875 & 8.3911 \\5 & 35 & 8.500 & 11.3767 \\6 & 18 & 7.875 & 6.9372 \\7 & 25 & 11.250 & 8.5815 \\8 & 30 & 7.875 & 9.5235 \\9 & 17 & 10.250 & 6.3640 \\10 & 22 & 9.500 & 7.8740 \\11 & 27 & 7.875 & 8.7086 \\12 & 26 & 12.875 & 9.3723\end{array}$$

-Referring to Table 18-8, an R chart is to be constructed for the time required to register. One way to create the upper control limit involves multiplying the average of the sample ranges by D4. For this data set, the value of D4 is______ .

Question 59

TABLE 18-8
Recently, a university switched to a new type of computer-based registration. The registrar is concerned with the amount of time students are spending on the computer registering under the new system. She decides to randomly select 8 students on each of the 12 days of the registration and determine the time each spends on the computer registering. The range, mean, and standard deviation of the times required to register are in the table that follows.
$$\begin{array} { c c l l } \text { Day } & \text { Range } & \text { Mean } & \text { Std.Dev. } \\1 & 10 & 5.250 & 3.4949 \\2 & 31 & 15.250 & 10.3060 \\3 & 13 & 20.375 & 4.9262 \\4 & 21 & 22.875 & 8.3911 \\5 & 35 & 8.500 & 11.3767 \\6 & 18 & 7.875 & 6.9372 \\7 & 25 & 11.250 & 8.5815 \\8 & 30 & 7.875 & 9.5235 \\9 & 17 & 10.250 & 6.3640 \\10 & 22 & 9.500 & 7.8740 \\11 & 27 & 7.875 & 8.7086 \\12 & 26 & 12.875 & 9.3723\end{array}$$

-Referring to Table 18-8, an X chart is to be used for the time required to register. The lower control limit for this data set is , while the upper control limit is__________ .

Question 60

TABLE 18-7
A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes samples of size 5 from each day's output and counts the number of blemishes on each silicone sheet. The results from 20 days of such evaluations are presented below.
Sheet
$\begin{array}{llllllllll}\text { Day } & 1 & 2 & 3 & 4 & 5 & \text { Mean } & \text { Range } \\\hline n1 & 8 & 10 & 14 & 6 & 5 & 8.6 & 9 \\2 & 8 & 13 & 6 & 6 & 10 & 8.6 & 7 \\3 & 10 & 12 & 7 & 7 & 9 & 9.0 & 5 \\4 & 5 & 9 & 12 & 7 & 10 & 8.6 & 7 \\5 & 8 & 3 & 8 & 9 & 10 & 7.6 & 7 \\6 & 9 & 7 & 9 & 6 & 9 & 8.0 & 3 \\7 & 10 & 10 & 5 & 7 & 6 & 7.6 & 5 \\8 & 10 & 9 & 10 & 6 & 5 & 8.0 & 5 \\9 & 6 & 10 & 6 & 9 & 9 & 8.0 & 4 \\10 & 6 & 9 & 8 & 6 & 8 & 7.4 & 3 \\11 & 8 & 5 & 6 & 10 & 10 & 7.8 & 5 \\12 & 6 & 4 & 7 & 7 & 12 & 7.2 & 8 \\13 & 7 & 5 & 7 & 6 & 9 & 6.8 & 4 \\14 & 5 & 8 & 8 & 7 & 6 & 6.8 & 3 \\15 & 7 & 12 & 10 & 6 & 10 & 9.0 & 6 \\16 & 7 & 11 & 4 & 7 & 8 & 7.4 & 7 \\17 & 8 & 4 & 5 & 4 & 7 & 5.6 & 4 \\18 & 11 & 4 & 11 & 11 & 10 & 9.4 & 7 \\19 & 6 & 10 & 6 & 10 & 10 & 8.4 & 4 \\20 & 6 & 12 & 12 & 6 & 8 & 8.8 & 6\end{array}$


She also decides that the upper specification limit is 10 blemishes.


-Referring to Table 18-7, an $\bar{X}$ chart is to be used for the number of blemishes. The lower control limit for this data set is , while the upper control limit is_____ .

Question 61

TABLE 18-8
Recently, a university switched to a new type of computer-based registration. The registrar is concerned with the amount of time students are spending on the computer registering under the new system. She decides to randomly select 8 students on each of the 12 days of the registration and determine the time each spends on the computer registering. The range, mean, and standard deviation of the times required to register are in the table that follows.
$$\begin{array} { c c l l } \text { Day } & \text { Range } & \text { Mean } & \text { Std.Dev. } \\1 & 10 & 5.250 & 3.4949 \\2 & 31 & 15.250 & 10.3060 \\3 & 13 & 20.375 & 4.9262 \\4 & 21 & 22.875 & 8.3911 \\5 & 35 & 8.500 & 11.3767 \\6 & 18 & 7.875 & 6.9372 \\7 & 25 & 11.250 & 8.5815 \\8 & 30 & 7.875 & 9.5235 \\9 & 17 & 10.250 & 6.3640 \\10 & 22 & 9.500 & 7.8740 \\11 & 27 & 7.875 & 8.7086 \\12 & 26 & 12.875 & 9.3723\end{array}$$

-Referring to Table 18-8, an R chart is to be constructed for the time required to register. One way to create the lower control limit involves multiplying the average of the sample ranges by D3. For this data set, the value of D3 is _____ .

Question 62

TABLE 18-7
A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes samples of size 5 from each day's output and counts the number of blemishes on each silicone sheet. The results from 20 days of such evaluations are presented below.
Sheet
$\begin{array}{llllllllll}\text { Day } & 1 & 2 & 3 & 4 & 5 & \text { Mean } & \text { Range } \\\hline1 & 8 & 10 & 14 & 6 & 5 & 8.6 & 9 \\2 & 8 & 13 & 6 & 6 & 10 & 8.6 & 7 \\3 & 10 & 12 & 7 & 7 & 9 & 9.0 & 5 \\4 & 5 & 9 & 12 & 7 & 10 & 8.6 & 7 \\5 & 8 & 3 & 8 & 9 & 10 & 7.6 & 7 \\6 & 9 & 7 & 9 & 6 & 9 & 8.0 & 3 \\7 & 10 & 10 & 5 & 7 & 6 & 7.6 & 5 \\8 & 10 & 9 & 10 & 6 & 5 & 8.0 & 5 \\9 & 6 & 10 & 6 & 9 & 9 & 8.0 & 4 \\10 & 6 & 9 & 8 & 6 & 8 & 7.4 & 3 \\11 & 8 & 5 & 6 & 10 & 10 & 7.8 & 5 \\12 & 6 & 4 & 7 & 7 & 12 & 7.2 & 8 \\13 & 7 & 5 & 7 & 6 & 9 & 6.8 & 4 \\14 & 5 & 8 & 8 & 7 & 6 & 6.8 & 3 \\15 & 7 & 12 & 10 & 6 & 10 & 9.0 & 6 \\16 & 7 & 11 & 4 & 7 & 8 & 7.4 & 7 \\17 & 8 & 4 & 5 & 4 & 7 & 5.6 & 4 \\18 & 11 & 4 & 11 & 11 & 10 & 9.4 & 7 \\19 & 6 & 10 & 6 & 10 & 10 & 8.4 & 4 \\20 & 6 & 12 & 12 & 6 & 8 & 8.8 & 6\end{array}$

She also decides that the upper specification limit is 10 blemishes.

-Referring to Table 18-7, an $\bar{X}$ chart is to be used for the number of blemishes. The center line of this chart is located at ______.

Question 63

TABLE 18-8
Recently, a university switched to a new type of computer-based registration. The registrar is concerned with the amount of time students are spending on the computer registering under the new system. She decides to randomly select 8 students on each of the 12 days of the registration and determine the time each spends on the computer registering. The range, mean, and standard deviation of the times required to register are in the table that follows.
$$\begin{array} { c c l l } \text { Day } & \text { Range } & \text { Mean } & \text { Std.Dev. } \\1 & 10 & 5.250 & 3.4949 \\2 & 31 & 15.250 & 10.3060 \\3 & 13 & 20.375 & 4.9262 \\4 & 21 & 22.875 & 8.3911 \\5 & 35 & 8.500 & 11.3767 \\6 & 18 & 7.875 & 6.9372 \\7 & 25 & 11.250 & 8.5815 \\8 & 30 & 7.875 & 9.5235 \\9 & 17 & 10.250 & 6.3640 \\10 & 22 & 9.500 & 7.8740 \\11 & 27 & 7.875 & 8.7086 \\12 & 26 & 12.875 & 9.3723\end{array}$$

-Referring to Table 18-8, an $\bar{X}$ chart is to be used for the time required to register. The center line of this chart is located at ______.

Question 64

TABLE 18-8
Recently, a university switched to a new type of computer-based registration. The registrar is concerned with the amount of time students are spending on the computer registering under the new system. She decides to randomly select 8 students on each of the 12 days of the registration and determine the time each spends on the computer registering. The range, mean, and standard deviation of the times required to register are in the table that follows.
$$\begin{array} { c c l l } \text { Day } & \text { Range } & \text { Mean } & \text { Std.Dev. } \\1 & 10 & 5.250 & 3.4949 \\2 & 31 & 15.250 & 10.3060 \\3 & 13 & 20.375 & 4.9262 \\4 & 21 & 22.875 & 8.3911 \\5 & 35 & 8.500 & 11.3767 \\6 & 18 & 7.875 & 6.9372 \\7 & 25 & 11.250 & 8.5815 \\8 & 30 & 7.875 & 9.5235 \\9 & 17 & 10.250 & 6.3640 \\10 & 22 & 9.500 & 7.8740 \\11 & 27 & 7.875 & 8.7086 \\12 & 26 & 12.875 & 9.3723\end{array}$$

-Referring to Table 18-8, construct an R chart for the time required to register.

Question 65

TABLE 18-7
A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes samples of size 5 from each day's output and counts the number of blemishes on each silicone sheet. The results from 20 days of such evaluations are presented below.
Sheet
$\begin{array}{llllllllll}\text { Day } & 1 & 2 & 3 & 4 & 5 & \text { Mean } & \text { Range } \\\hline1 & 8 & 10 & 14 & 6 & 5 & 8.6 & 9 \\2 & 8 & 13 & 6 & 6 & 10 & 8.6 & 7 \\3 & 10 & 12 & 7 & 7 & 9 & 9.0 & 5 \\4 & 5 & 9 & 12 & 7 & 10 & 8.6 & 7 \\5 & 8 & 3 & 8 & 9 & 10 & 7.6 & 7 \\6 & 9 & 7 & 9 & 6 & 9 & 8.0 & 3 \\7 & 10 & 10 & 5 & 7 & 6 & 7.6 & 5 \\8 & 10 & 9 & 10 & 6 & 5 & 8.0 & 5 \\9 & 6 & 10 & 6 & 9 & 9 & 8.0 & 4 \\10 & 6 & 9 & 8 & 6 & 8 & 7.4 & 3 \\11 & 8 & 5 & 6 & 10 & 10 & 7.8 & 5 \\12 & 6 & 4 & 7 & 7 & 12 & 7.2 & 8 \\13 & 7 & 5 & 7 & 6 & 9 & 6.8 & 4 \\14 & 5 & 8 & 8 & 7 & 6 & 6.8 & 3 \\15 & 7 & 12 & 10 & 6 & 10 & 9.0 & 6 \\16 & 7 & 11 & 4 & 7 & 8 & 7.4 & 7 \\17 & 8 & 4 & 5 & 4 & 7 & 5.6 & 4 \\18 & 11 & 4 & 11 & 11 & 10 & 9.4 & 7 \\19 & 6 & 10 & 6 & 10 & 10 & 8.4 & 4 \\20 & 6 & 12 & 12 & 6 & 8 & 8.8 & 6\end{array}$
She also decides that the upper specification limit is 10 blemishes.

-Referring to Table 18-7, an R chart is to be constructed for the number of blemishes. One way to create the upper control limit involves multiplying the average of the sample ranges by D4. For this data set, the value of D₄ is ______ .

Question 66

TABLE 18-4
A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.
$$\begin{array} { l l l } \text { Hour } & \bar { X } &R\\\hline 1 & 18.4 & 25 \\2 & 16.9 & 27 \\3 & 23.0 & 30 \\4 & 21.2 & 23 \\5 & 21.0 & 24 \\6 & 24.0 & 25 \\7 & 19.3 & 12 \\8 & 15.8 & 14 \\9 & 20.0 & 13 \\10 & 23.0 & 11\end{array}$$ She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively.

-Referring to Table 18-4, what is the value of the Cp index?

Question 67

TABLE 18-7
A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes samples of size 5 from each day's output and counts the number of blemishes on each silicone sheet. The results from 20 days of such evaluations are presented below.
Sheet
$\begin{array}{llllllllll}\text { Day } & 1 & 2 & 3 & 4 & 5 & \text { Mean } & \text { Range } \\\hline1 & 8 & 10 & 14 & 6 & 5 & 8.6 & 9 \\2 & 8 & 13 & 6 & 6 & 10 & 8.6 & 7 \\3 & 10 & 12 & 7 & 7 & 9 & 9.0 & 5 \\4 & 5 & 9 & 12 & 7 & 10 & 8.6 & 7 \\5 & 8 & 3 & 8 & 9 & 10 & 7.6 & 7 \\6 & 9 & 7 & 9 & 6 & 9 & 8.0 & 3 \\7 & 10 & 10 & 5 & 7 & 6 & 7.6 & 5 \\8 & 10 & 9 & 10 & 6 & 5 & 8.0 & 5 \\9 & 6 & 10 & 6 & 9 & 9 & 8.0 & 4 \\10 & 6 & 9 & 8 & 6 & 8 & 7.4 & 3 \\11 & 8 & 5 & 6 & 10 & 10 & 7.8 & 5 \\12 & 6 & 4 & 7 & 7 & 12 & 7.2 & 8 \\13 & 7 & 5 & 7 & 6 & 9 & 6.8 & 4 \\14 & 5 & 8 & 8 & 7 & 6 & 6.8 & 3 \\15 & 7 & 12 & 10 & 6 & 10 & 9.0 & 6 \\16 & 7 & 11 & 4 & 7 & 8 & 7.4 & 7 \\17 & 8 & 4 & 5 & 4 & 7 & 5.6 & 4 \\18 & 11 & 4 & 11 & 11 & 10 & 9.4 & 7 \\19 & 6 & 10 & 6 & 10 & 10 & 8.4 & 4 \\20 & 6 & 12 & 12 & 6 & 8 & 8.8 & 6\end{array}$

She also decides that the upper specification limit is 10 blemishes.

-Referring to Table 18-7, what percentage of the chips will fall below the upper specification limit?

Question 68

TABLE 18-7
A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes samples of size 5 from each day's output and counts the number of blemishes on each silicone sheet. The results from 20 days of such evaluations are presented below.
Sheet
$\begin{array}{llllllllll}\text { Day } & 1 & 2 & 3 & 4 & 5 & \text { Mean } & \text { Range } \\\hline1 & 8 & 10 & 14 & 6 & 5 & 8.6 & 9 \\2 & 8 & 13 & 6 & 6 & 10 & 8.6 & 7 \\3 & 10 & 12 & 7 & 7 & 9 & 9.0 & 5 \\4 & 5 & 9 & 12 & 7 & 10 & 8.6 & 7 \\5 & 8 & 3 & 8 & 9 & 10 & 7.6 & 7 \\6 & 9 & 7 & 9 & 6 & 9 & 8.0 & 3 \\7 & 10 & 10 & 5 & 7 & 6 & 7.6 & 5 \\8 & 10 & 9 & 10 & 6 & 5 & 8.0 & 5 \\9 & 6 & 10 & 6 & 9 & 9 & 8.0 & 4 \\10 & 6 & 9 & 8 & 6 & 8 & 7.4 & 3 \\11 & 8 & 5 & 6 & 10 & 10 & 7.8 & 5 \\12 & 6 & 4 & 7 & 7 & 12 & 7.2 & 8 \\13 & 7 & 5 & 7 & 6 & 9 & 6.8 & 4 \\14 & 5 & 8 & 8 & 7 & 6 & 6.8 & 3 \\15 & 7 & 12 & 10 & 6 & 10 & 9.0 & 6 \\16 & 7 & 11 & 4 & 7 & 8 & 7.4 & 7 \\17 & 8 & 4 & 5 & 4 & 7 & 5.6 & 4 \\18 & 11 & 4 & 11 & 11 & 10 & 9.4 & 7 \\19 & 6 & 10 & 6 & 10 & 10 & 8.4 & 4 \\20 & 6 & 12 & 12 & 6 & 8 & 8.8 & 6\end{array}$

She also decides that the upper specification limit is 10 blemishes.

-Referring to Table 18-7, what is the value of d₂ factor?

Question 69

TABLE 18-9
The manufacturer of cat food constructed control charts and analyzed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 pounds. The table below provides the range and mean of the weights of five cans tested every fifteen minutes during a day's production.
$\begin{array}{cclccc}\text { Number } & \text { XBar } & \text { Range } & \text { Number } & \text { XBar } & \text { Range } \\\hline 1 & 3.05072 & 0.0215 & 16 & 3.04646 & 0.073 \\2 & 3.01228 & 0.087 & 17 & 3.03868 & 0.0696 \\3 & 3.03558 & 0.0851 & 18 & 3.03338 & 0.0329 \\4 & 3.01014 & 0.0674 & 19 & 3.03322 & 0.0455 \\5 & 3.00858 & 0.0983 & 20 & 3.05078 & 0.0215 \\6 & 3.02704 & 0.0527 & 21 & 3.04808 & 0.0396 \\7 & 3.04268 & 0.0508 & 22 & 3.05348 & 0.0581 \\8 & 3.01052 & 0.0791 & 23 & 3.05516 & 0.0682 \\9 & 3.03464 & 0.0663 & 24 & 3.03426 & 0.0325 \\10 & 3.02034 & 0.0538 & 25 & 3.0516 & 0.0641 \\11 & 3.03764 & 0.0584 & 26 & 3.05562 & 0.0809 \\12 & 3.0409 & 0.0434 & 27 & 3.04402 & 0.0374 \\13 & 3.0519 & 0.0762 & 28 & 3.06458 & 0.0284 \\14 & 3.03994 & 0.0833 & 29 & 3.0544 & 0.0738 \\15 & 3.03788 & 0.0601 & & & \\\hline\end{array}$


-Referring to Table 18-9, an X chart is to be used for the weight. The lower control limit for this data set is_____ , while the upper control limit is_____ .

Question 70

TABLE 18-9
The manufacturer of cat food constructed control charts and analyzed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 pounds. The table below provides the range and mean of the weights of five cans tested every fifteen minutes during a day's production.
$\begin{array}{cllccc}\hline \text { Number } & \text { XBar } & \text { Range } & \text { Number } & \text { XBar } & \text { Range } \\\hline 1 & 3.05072 & 0.0215 & 16 & 3.04646 & 0.073 \\2 & 3.01228 & 0.087 & 17 & 3.03868 & 0.0696 \\3 & 3.03558 & 0.0851 & 18 & 3.03338 & 0.0329 \\4 & 3.01014 & 0.0674 & 19 & 3.03322 & 0.0455 \\5 & 3.00858 & 0.0983 & 20 & 3.05078 & 0.0215 \\6 & 3.02704 & 0.0527 & 21 & 3.04808 & 0.0396 \\7 & 3.04268 & 0.0508 & 22 & 3.05348 & 0.0581 \\8 & 3.01052 & 0.0791 & 23 & 3.05516 & 0.0682 \\9 & 3.03464 & 0.0663 & 24 & 3.03426 & 0.0325 \\10 & 3.02034 & 0.0538 & 25 & 3.0516 & 0.0641 \\11 & 3.03764 & 0.0584 & 26 & 3.05562 & 0.0809 \\12 & 3.0409 & 0.0434 & 27 & 3.04402 & 0.0374 \\13 & 3.0519 & 0.0762 & 28 & 3.06458 & 0.0284 \\14 & 3.03994 & 0.0833 & 29 & 3.0544 & 0.0738 \\15 & 3.03788 & 0.0601 & & & \\\hline\end{array}$





-Referring to Table 18-9, an $\bar{ X}$ chart is to be used for the weight. One way to obtain the control limits is to take the grand mean and add and subtract the product of A2 times the average of the sample ranges. For this data set, the value of A2 is_____ .

Question 71

TABLE 18-7
A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes samples of size 5 from each day's output and counts the number of blemishes on each silicone sheet. The results from 20 days of such evaluations are presented below.
Sheet
$\begin{array}{llllllllll}\text { Day } & 1 & 2 & 3 & 4 & 5 & \text { Mean } & \text { Range } \\\hline1 & 8 & 10 & 14 & 6 & 5 & 8.6 & 9 \\2 & 8 & 13 & 6 & 6 & 10 & 8.6 & 7 \\3 & 10 & 12 & 7 & 7 & 9 & 9.0 & 5 \\4 & 5 & 9 & 12 & 7 & 10 & 8.6 & 7 \\5 & 8 & 3 & 8 & 9 & 10 & 7.6 & 7 \\6 & 9 & 7 & 9 & 6 & 9 & 8.0 & 3 \\7 & 10 & 10 & 5 & 7 & 6 & 7.6 & 5 \\8 & 10 & 9 & 10 & 6 & 5 & 8.0 & 5 \\9 & 6 & 10 & 6 & 9 & 9 & 8.0 & 4 \\10 & 6 & 9 & 8 & 6 & 8 & 7.4 & 3 \\11 & 8 & 5 & 6 & 10 & 10 & 7.8 & 5 \\12 & 6 & 4 & 7 & 7 & 12 & 7.2 & 8 \\13 & 7 & 5 & 7 & 6 & 9 & 6.8 & 4 \\14 & 5 & 8 & 8 & 7 & 6 & 6.8 & 3 \\15 & 7 & 12 & 10 & 6 & 10 & 9.0 & 6 \\16 & 7 & 11 & 4 & 7 & 8 & 7.4 & 7 \\17 & 8 & 4 & 5 & 4 & 7 & 5.6 & 4 \\18 & 11 & 4 & 11 & 11 & 10 & 9.4 & 7 \\19 & 6 & 10 & 6 & 10 & 10 & 8.4 & 4 \\20 & 6 & 12 & 12 & 6 & 8 & 8.8 & 6\end{array}$
She also decides that the upper specification limit is 10 blemishes.

-Referring to Table 18-7, an R chart is to be constructed for the number of blemishes. One way to create the lower control limit involves multiplying the average of the sample ranges by D3. For this data set, the value of D3 is ____ .

Question 72

TABLE 18-9
The manufacturer of cat food constructed control charts and analyzed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 pounds. The table below provides the range and mean of the weights of five cans tested every fifteen minutes during a day's production.
$\begin{array}{cclccc}\text { Number } & \text { XBar } & \text { Range } & \text { Number } & \text { XBar } & \text { Range } \\\hline 1 & 3.05072 & 0.0215 & 16 & 3.04646 & 0.073 \\2 & 3.01228 & 0.087 & 17 & 3.03868 & 0.0696 \\3 & 3.03558 & 0.0851 & 18 & 3.03338 & 0.0329 \\4 & 3.01014 & 0.0674 & 19 & 3.03322 & 0.0455 \\5 & 3.00858 & 0.0983 & 20 & 3.05078 & 0.0215 \\6 & 3.02704 & 0.0527 & 21 & 3.04808 & 0.0396 \\7 & 3.04268 & 0.0508 & 22 & 3.05348 & 0.0581 \\8 & 3.01052 & 0.0791 & 23 & 3.05516 & 0.0682 \\9 & 3.03464 & 0.0663 & 24 & 3.03426 & 0.0325 \\10 & 3.02034 & 0.0538 & 25 & 3.0516 & 0.0641 \\11 & 3.03764 & 0.0584 & 26 & 3.05562 & 0.0809 \\12 & 3.0409 & 0.0434 & 27 & 3.04402 & 0.0374 \\13 & 3.0519 & 0.0762 & 28 & 3.06458 & 0.0284 \\14 & 3.03994 & 0.0833 & 29 & 3.0544 & 0.0738 \\15 & 3.03788 & 0.0601 & & & \\\hline\end{array}$




-Referring to Table 18-9, an R chart is to be constructed for the weight. One way to create the upper control limit involves multiplying the average of the sample ranges by D4. For this data set, the value of D4 is _____ .

Question 73

TABLE 18-9
The manufacturer of cat food constructed control charts and analyzed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 pounds. The table below provides the range and mean of the weights of five cans tested every fifteen minutes during a day's production.
$\begin{array}{cclccc}\text { Number } & \text { XBar } & \text { Range } & \text { Number } & \text { XBar } & \text { Range } \\\hline 1 & 3.05072 & 0.0215 & 16 & 3.04646 & 0.073 \\2 & 3.01228 & 0.087 & 17 & 3.03868 & 0.0696 \\3 & 3.03558 & 0.0851 & 18 & 3.03338 & 0.0329 \\4 & 3.01014 & 0.0674 & 19 & 3.03322 & 0.0455 \\5 & 3.00858 & 0.0983 & 20 & 3.05078 & 0.0215 \\6 & 3.02704 & 0.0527 & 21 & 3.04808 & 0.0396 \\7 & 3.04268 & 0.0508 & 22 & 3.05348 & 0.0581 \\8 & 3.01052 & 0.0791 & 23 & 3.05516 & 0.0682 \\9 & 3.03464 & 0.0663 & 24 & 3.03426 & 0.0325 \\10 & 3.02034 & 0.0538 & 25 & 3.0516 & 0.0641 \\11 & 3.03764 & 0.0584 & 26 & 3.05562 & 0.0809 \\12 & 3.0409 & 0.0434 & 27 & 3.04402 & 0.0374 \\13 & 3.0519 & 0.0762 & 28 & 3.06458 & 0.0284 \\14 & 3.03994 & 0.0833 & 29 & 3.0544 & 0.0738 \\15 & 3.03788 & 0.0601 & & & \\\hline\end{array}$





-Referring to Table 18-9, an R chart is to be constructed for the weight. The center line of this R chart is located at ______.

Question 74

TABLE 18-7
A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes samples of size 5 from each day's output and counts the number of blemishes on each silicone sheet. The results from 20 days of such evaluations are presented below.
Sheet
$\begin{array}{llllllllll}\text { Day } & 1 & 2 & 3 & 4 & 5 & \text { Mean } & \text { Range } \\\hline1 & 8 & 10 & 14 & 6 & 5 & 8.6 & 9 \\2 & 8 & 13 & 6 & 6 & 10 & 8.6 & 7 \\3 & 10 & 12 & 7 & 7 & 9 & 9.0 & 5 \\4 & 5 & 9 & 12 & 7 & 10 & 8.6 & 7 \\5 & 8 & 3 & 8 & 9 & 10 & 7.6 & 7 \\6 & 9 & 7 & 9 & 6 & 9 & 8.0 & 3 \\7 & 10 & 10 & 5 & 7 & 6 & 7.6 & 5 \\8 & 10 & 9 & 10 & 6 & 5 & 8.0 & 5 \\9 & 6 & 10 & 6 & 9 & 9 & 8.0 & 4 \\10 & 6 & 9 & 8 & 6 & 8 & 7.4 & 3 \\11 & 8 & 5 & 6 & 10 & 10 & 7.8 & 5 \\12 & 6 & 4 & 7 & 7 & 12 & 7.2 & 8 \\13 & 7 & 5 & 7 & 6 & 9 & 6.8 & 4 \\14 & 5 & 8 & 8 & 7 & 6 & 6.8 & 3 \\15 & 7 & 12 & 10 & 6 & 10 & 9.0 & 6 \\16 & 7 & 11 & 4 & 7 & 8 & 7.4 & 7 \\17 & 8 & 4 & 5 & 4 & 7 & 5.6 & 4 \\18 & 11 & 4 & 11 & 11 & 10 & 9.4 & 7 \\19 & 6 & 10 & 6 & 10 & 10 & 8.4 & 4 \\20 & 6 & 12 & 12 & 6 & 8 & 8.8 & 6\end{array}$

She also decides that the upper specification limit is 10 blemishes.

-Referring to Table 18-7, an R chart is to be constructed for the number of blemishes. The lower control limit for this data set is ____.

Question 75

TABLE 18-5
A manufacturer of computer disks took samples of 240 disks on 15 consecutive days. The number of disks with bad sectors was determined for each of these samples. The results are in the table that follows.
$$\begin{array}{l}\text { Day Bad \% Bad }\\\begin{array} { r r r } \hline 1 & 9 & 0.037500 \\2 & 7 & 0.029167 \\3 & 4 & 0.016667 \\4 & 6 & 0.025000 \\5 & 8 & 0.033333 \\6 & 3 & 0.012500 \\7 & 6 & 0.025000 \\8 & 10 & 0.041667 \\9 & 16 & 0.066667 \\10 & 24 & 0.100000 \\11 & 15 & 0.062500 \\12 & 9 & 0.037500 \\13 & 4 & 0.016667 \\14 & 8 & 0.033333 \\15 & 6 & 0.025000\end{array}\end{array}$$

-Referring to Table 18-5, the best estimate of the average proportion of disks with bad sectors is ____ .

Question 76

The cause of variation that can be reduced only by changing the system is ______ cause variation.

Question 77

TABLE 18-4
A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.

$\begin{array} { l l l }\text { Hour }&\bar{X} &R\\ \hline 1 & 18.4 & 25 \\ 2 & 16.9 & 27 \\ 3 & 23.0 & 30 \\ 4 & 21.2 & 23 \\ 5 & 21.0 & 24 \\ 6 & 24.0 & 25 \\ 7 & 19.3 & 12 \\ 8 & 15.8 & 14 \\ 9 & 20.0 & 13 \\ 10 & 23.0 & 11 \end{array}$
She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively.

-Referring to Table 18-4, what is the value of d2 factor?

Question 78

________causes of variation are correctable without modifying the system.

Question 79

TABLE 18-7
A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes samples of size 5 from each day's output and counts the number of blemishes on each silicone sheet. The results from 20 days of such evaluations are presented below.
Sheet
$\begin{array}{llllllllll}\text { Day } & 1 & 2 & 3 & 4 & 5 & \text { Mean } & \text { Range } \\\hline n1 & 8 & 10 & 14 & 6 & 5 & 8.6 & 9 \\2 & 8 & 13 & 6 & 6 & 10 & 8.6 & 7 \\3 & 10 & 12 & 7 & 7 & 9 & 9.0 & 5 \\4 & 5 & 9 & 12 & 7 & 10 & 8.6 & 7 \\5 & 8 & 3 & 8 & 9 & 10 & 7.6 & 7 \\6 & 9 & 7 & 9 & 6 & 9 & 8.0 & 3 \\7 & 10 & 10 & 5 & 7 & 6 & 7.6 & 5 \\8 & 10 & 9 & 10 & 6 & 5 & 8.0 & 5 \\9 & 6 & 10 & 6 & 9 & 9 & 8.0 & 4 \\10 & 6 & 9 & 8 & 6 & 8 & 7.4 & 3 \\11 & 8 & 5 & 6 & 10 & 10 & 7.8 & 5 \\12 & 6 & 4 & 7 & 7 & 12 & 7.2 & 8 \\13 & 7 & 5 & 7 & 6 & 9 & 6.8 & 4 \\14 & 5 & 8 & 8 & 7 & 6 & 6.8 & 3 \\15 & 7 & 12 & 10 & 6 & 10 & 9.0 & 6 \\16 & 7 & 11 & 4 & 7 & 8 & 7.4 & 7 \\17 & 8 & 4 & 5 & 4 & 7 & 5.6 & 4 \\18 & 11 & 4 & 11 & 11 & 10 & 9.4 & 7 \\19 & 6 & 10 & 6 & 10 & 10 & 8.4 & 4 \\20 & 6 & 12 & 12 & 6 & 8 & 8.8 & 6\end{array}$


She also decides that the upper specification limit is 10 blemishes.


-Referring to Table 18-7, an $\bar{X}$ chart is to be used for the number of blemishes. One way to obtain the control limits is to take the grand mean and add and subtract the product of A2 times the average of the sample ranges. For this data set, the value of A2 is______ .

Question 80

TABLE 18-9
The manufacturer of cat food constructed control charts and analyzed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 pounds. The table below provides the range and mean of the weights of five cans tested every fifteen minutes during a day's production.
$\begin{array}{cclccc}\text { Number } & \text { XBar } & \text { Range } & \text { Number } & \text { XBar } & \text { Range } \\\hline 1 & 3.05072 & 0.0215 & 16 & 3.04646 & 0.073 \\2 & 3.01228 & 0.087 & 17 & 3.03868 & 0.0696 \\3 & 3.03558 & 0.0851 & 18 & 3.03338 & 0.0329 \\4 & 3.01014 & 0.0674 & 19 & 3.03322 & 0.0455 \\5 & 3.00858 & 0.0983 & 20 & 3.05078 & 0.0215 \\6 & 3.02704 & 0.0527 & 21 & 3.04808 & 0.0396 \\7 & 3.04268 & 0.0508 & 22 & 3.05348 & 0.0581 \\8 & 3.01052 & 0.0791 & 23 & 3.05516 & 0.0682 \\9 & 3.03464 & 0.0663 & 24 & 3.03426 & 0.0325 \\ 10 & 3.02034 & 0.0538 & 25 & 3.0516 & 0.0641 \\11 & 3.03764 & 0.0584 & 26 & 3.05562 & 0.0809 \\12 & 3.0409 & 0.0434 & 27 & 3.04402 & 0.0374 \\13 & 3.0519 & 0.0762 & 28 & 3.06458 & 0.0284 \\14 & 3.03994 & 0.0833 & 29 & 3.0544 & 0.0738 \\15 & 3.03788 & 0.0601 & & & \\\hline\end{array}$



-Referring to Table 18-9, an R chart is to be constructed for the weight. One way to create the lower control limit involves multiplying the average of the sample ranges by D3. For this data set, the value of D3 is _____ .