Deck 18: Statistical Applications in Quality Management

Question 1

SCENARIO 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 for one
of the delivery boys and construct a p chart to see whether the percentage is too erratic.
Number of Papers $$\begin{array}{l}\begin{array} { r r } &\text { Number of Papers }\\ \underline{ \text { Day } } & \underline{ \text { Delivered} } \\ 1 & 46 \\2 & 45 \\3 & 46 \\4 & 45 \\5 & 43 \\6 & 48 \\7 & 46 \\8 & 49 \\9 & 48 \\10 & 47\end{array}\end{array}$$

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

A) 0.926
B) 0.961
C) 0.979
D) 1.037

Answer 1

1.037

Question 2

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.

Answer 2

C

Question 3

SCENARIO 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. $\begin{array}{ccc} \underline{\text { Day } }& \underline{\bar{X} \text { (in minutes) }} & \underline{\text {R}}\\1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$


-Referring to Scenario 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) 4.8
B) 6.0
C) 6.9
D) 7.1

Answer 3

6.0

Question 4

One of the morals of the red bead experiment is:

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

Question 5

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

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

Question 6

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 points fall outside the lower control limit.
C) A control chart in which several points fall outside the upper control limit.
D) All of the above.

Question 7

SCENARIO 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 for one
of the delivery boys and construct a p chart to see whether the percentage is too erratic.
Number of Papers $$\begin{array}{l}\begin{array} { r r } &\text { Number of Papers }\\ \underline{ \text { Day } } & \underline{ \text { Delivered} } \\ 1 & 46 \\2 & 45 \\3 & 46 \\4 & 45 \\5 & 43 \\6 & 48 \\7 & 46 \\8 & 49 \\9 & 48 \\10 & 47\end{array}\end{array}$$

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

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

Question 8

SCENARIO 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 for one
of the delivery boys and construct a p chart to see whether the percentage is too erratic.
Number of Papers $$\begin{array}{l}\begin{array} { r r } &\text { Number of Papers }\\ \underline{ \text { Day } } & \underline{ \text { Delivered} } \\ 1 & 46 \\2 & 45 \\3 & 46 \\4 & 45 \\5 & 43 \\6 & 48 \\7 & 46 \\8 & 49 \\9 & 48 \\10 & 47\end{array}\end{array}$$

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

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

Question 9

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

A) Special or assignable causes
B) Common causes
C) Total causes
D) None of the above

Question 10

SCENARIO 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. $$\begin{array} { c c } \begin{array} { c } \text { Sample } \\\underline{\text { (Day) }}\end{array} & \begin{array} { c } \text { Number Favoring } \\\underline{\text { Incumbent Candidate }}\end{array} \\ 1 & 57 \\2 & 57 \\3 & 53 \\4 & 51 \\5 & 55 \\6 & 60 \\7 & 56 \\8 & 59\end{array}$$

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

A) In-control
B) Increasing trend
C) Decreasing trend
D) Individual outliers

Question 11

The control chart

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

Question 12

SCENARIO 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 for one
of the delivery boys and construct a p chart to see whether the percentage is too erratic.
Number of Papers $$\begin{array}{l}\begin{array} { r r } &\text { Number of Papers }\\ \underline{ \text { Day } } & \underline{ \text { Delivered} } \\ 1 & 46 \\2 & 45 \\3 & 46 \\4 & 45 \\5 & 43 \\6 & 48 \\7 & 46 \\8 & 49 \\9 & 48 \\10 & 47\end{array}\end{array}$$

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

A) Cycles
B) Increasing trend
C) In-control
D) Individual outliers

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 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 no points fall outside either the upper control limit or the lower control limit and no patterns are present.
C) A control chart in which several points fall outside the upper control limit.
D) All of the above.

Question 14

SCENARIO 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. $\begin{array}{ccc} \underline{\text { Day } }& \underline{\bar{X} \text { (in minutes) }} & \underline{\text {R}}\\1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$


-Referring to Scenario 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) 10.66
B) 9.37
C) 7.98
D) 6.34

Question 15

SCENARIO 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. $$\begin{array} { c c } \begin{array} { c } \text { Sample } \\\underline{\text { (Day) }}\end{array} & \begin{array} { c } \text { Number Favoring } \\\underline{\text { Incumbent Candidate }}\end{array} \\ 1 & 57 \\2 & 57 \\3 & 53 \\4 & 51 \\5 & 55 \\6 & 60 \\7 & 56 \\8 & 59\end{array}$$

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

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

Question 16

SCENARIO 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. $$\begin{array} { c c } \begin{array} { c } \text { Sample } \\\underline{\text { (Day) }}\end{array} & \begin{array} { c } \text { Number Favoring } \\\underline{\text { Incumbent Candidate }}\end{array} \\ 1 & 57 \\2 & 57 \\3 & 53 \\4 & 51 \\5 & 55 \\6 & 60 \\7 & 56 \\8 & 59\end{array}$$

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

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

Question 17

SCENARIO 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. $$\begin{array} { c c } \begin{array} { c } \text { Sample } \\\underline{\text { (Day) }}\end{array} & \begin{array} { c } \text { Number Favoring } \\\underline{\text { Incumbent Candidate }}\end{array} \\ 1 & 57 \\2 & 57 \\3 & 53 \\4 & 51 \\5 & 55 \\6 & 60 \\7 & 56 \\8 & 59\end{array}$$

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

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

Question 18

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

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

Question 19

SCENARIO 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. $\begin{array}{ccc} \underline{\text { Day } }& \underline{\bar{X} \text { (in minutes) }} & \underline{\text {R}}\\1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$


-Referring to Scenario 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) 4.84
B) 3.37
C) 2.98
D) 1.34

Question 20

A process is said to be out of control if

A) a point falls above the upper or below the lower control lines.
B) eight or more consecutive points fall above the center line or eight or more consecutive points fall below the center line.
C) Either of the above.
D) None of the above.

Question 21

SCENARIO 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. She also decides that lower and upper specification limit for the critical-to-quality variable should be
10 and 30 seconds, respectively.
Referring to Scenario 18-4, what is the value of the CPU index?

Question 22

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

-Referring to Scenario 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) 20.00
B) 20.56
C) 20.40
D) 24.00

Question 23

SCENARIO 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. She also decides that lower and upper specification limit for the critical-to-quality variable should be
10 and 30 seconds, respectively.
Referring to Scenario 18-4, what is the value of the index?

Question 24

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

-Referring to Scenario 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 increase; UCL would decrease.
B) LCL would remain the same; UCL would decrease.
C) Both LCL and UCL would remain the same.
D) LCL would decrease; UCL would increase.

Question 25

SCENARIO 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. She also decides that lower and upper specification limit for the critical-to-quality variable should be
10 and 30 seconds, respectively.
Referring to Scenario 18-4, what is the value of the CPL index?

Question 26

SCENARIO 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. $\begin{array}{ccc} \underline{\text { Day } }& \underline{\bar{X} \text { (in minutes) }} & \underline{\text {R}}\\1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$


-Referring to Scenario 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) Increasing trend
B) Decreasing trend
C) In-control
D) Points outside the control limits

Question 27

SCENARIO 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. $\begin{array}{ccc} \underline{\text { Day } }& \underline{\bar{X} \text { (in minutes) }} & \underline{\text {R}}\\1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$


-Referring to Scenario 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) 56.15
C) 57.15
D) 58.05

Question 28

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

-Referring to Scenario 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) - 2.33, 43.13
B) - 2.28, 42.28
C) 0, 42.28
D) 0, 43.13

Question 29

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

-Referring to Scenario 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) Decreasing trend
B) Increasing trend
C) In-control
D) Individual outliers

Question 30

SCENARIO 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. She also decides that lower and upper specification limit for the critical-to-quality variable should be
10 and 30 seconds, respectively.
Referring to Scenario 18-4, what is the value of factor?

Question 31

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

-Referring to Scenario 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) Decreasing trend
B) In-control
C) Increasing trend
D) Individual outliers

Question 32

SCENARIO 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. $\begin{array}{ccc} \underline{\text { Day } }& \underline{\bar{X} \text { (in minutes) }} & \underline{\text {R}}\\1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$


-Referring to Scenario 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 increase; UCL would decrease.
B) LCL would remain the same; UCL would decrease.
C) Both LCL and UCL would remain the same.
D) LCL would decrease; UCL would increase.

Question 33

SCENARIO 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. She also decides that lower and upper specification limit for the critical-to-quality variable should be
10 and 30 seconds, respectively.
Referring to Scenario 18-4, what is the value of the index?

Question 34

The control limits are based on the standard deviation of the process.

Question 35

SCENARIO 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. $\begin{array}{ccc} \underline{\text { Day } }& \underline{\bar{X} \text { (in minutes) }} & \underline{\text {R}}\\1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$


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

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

Question 36

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

-Referring to Scenario 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) 20.00
B) 20.26
C) 21.00
D) 24.26

Question 37

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

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

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

Question 38

SCENARIO 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. $\begin{array}{ccc} \underline{\text { Day } }& \underline{\bar{X} \text { (in minutes) }} & \underline{\text {R}}\\1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$


-Referring to Scenario 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) 59.5
C) 58.0
D) 57.1

Question 39

SCENARIO 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. She also decides that lower and upper specification limit for the critical-to-quality variable should be
10 and 30 seconds, respectively.
Referring to Scenario 18-4, what percentage of the time it takes workers to complete an important
production task will fall inside the specification limits?

Question 40

SCENARIO 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. $\begin{array}{ccc} \underline{\text { Day } }& \underline{\bar{X} \text { (in minutes) }} & \underline{\text {R}}\\1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$


-Referring to Scenario 18-3, suppose the analyst constructs an $\bar { X }$ chart to see if the production process is in-control. Which expression best describes this chart?

A) In-control
B) Increasing trend
C) Decreasing trend
D) Individual outliers

Question 41

In the United States, the control limits on a control chart are placed so that they are
3 standard deviations above and below a central line.

Question 42

_______ causes of variation are correctable without modifying the system.

Question 43

One of the morals of the red bead experiment is that variation is part of any
process.

Question 44

It is not possible for the $\bar { X }$ chart to be out-of-control when the R chart is in control.

Question 45

Special or assignable causes of variation are signaled by individual fluctuations or
patterns in the data.

Question 46

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

Question 47

SCENARIO 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.
Referring to Scenario 18-5, construct a p control chart for these data.

Question 48

The purpose of a control chart is to eliminate common cause variation.

Question 49

SCENARIO 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.
Referring to Scenario 18-5, the best estimate of the mean proportion of disks with bad sectors is
__________.

Question 50

SCENARIO 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 follow.
Referring to Scenario 18-6, the estimate of the proportion of poor quality bags of candy is
__________.

Question 51

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

Question 52

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

Question 53

The p chart is a control chart used for monitoring the proportion of items that meet
given specifications.

Question 54

SCENARIO 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.
Referring to Scenario 18-5, a p control chart is to be made for these data. The upper control limit
is __________, and the lower control limit is __________.

Question 55

The R chart is a control chart used to monitor a process mean.

Question 56

SCENARIO 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. $\begin{array}{ccc} \underline{\text { Day }}& \underline{\text { Bad }} & \underline{ \% \mathrm{Bad}}\\1 & 9 & 0.037500 \\2 & 7 & 0.029167 \\3 & 4 & 0.016667 \\4 & 6 & 0.025000 \\5 & 8 & 0.033333 \\6 & 3 & 0.012500 \\7 & 6 & 0.025000 \\8 & 10 & 0.041667 \\9 & 16 & 0.06667 \\10 & 24 & 0.100000 \\11 & 15 & 0.062500 \\12 & 9 & 0.037500 \\13 & 4 & 0.016667 \\14 & 8 & 0.033333 \\15 & 6 & 0.025000\end{array}$


-Referring to Scenario 18-5, the process seems to be in control.

Question 57

Common causes of variation are correctable without modifying the system.

Question 58

Changes in the system to reduce common cause variation are the responsibility of
management.

Question 59

SCENARIO 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.
Referring to Scenario 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 60

Common causes of variation represent variation due to the inherent variability in
the system.

Question 61

SCENARIO 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. $$\begin{array}{l}\text {\quad\quad\quad\quad\quad\quad\quad Sheet }\\\begin{array} { r r r r r r r r } \underline {\text { Day } }& \underline { 1 } &\underline { 2 }&\underline { 3 }& \underline {4 }& \underline {5} & \underline { \text { Mean } } &\underline { \text { Range }} \\1 & 8 & 10 & 14 & 6 & 5 & 8.6 & 9 \\2 & 8 & 13 & 6 & 6 & 10 & 8.6 & 7 \\3 & 10 & 12 & 7 & 7 & 9 & 9.0 & 5 \\4 & 5 & 9 & 12 & 7 & 10 & 8.6 & 7 \\5 & 8 & 3 & 8 & 9 & 10 & 7.6 & 7 \\6 & 9 & 7 & 9 & 6 & 9 & 8.0 & 3 \\7 & 10 & 10 & 5 & 7 & 6 & 7.6 & 5 \\8 & 10 & 9 & 10 & 6 & 5 & 8.0 & 5 \\9 & 6 & 10 & 6 & 9 & 9 & 8.0 & 4 \\10 & 6 & 9 & 8 & 6 & 8 & 7.4 & 3 \\11 & 8 & 5 & 6 & 10 & 10 & 7.8 & 5 \\12 & 6 & 4 & 7 & 7 & 12 & 7.2 & 8 \\13 & 7 & 5 & 7 & 6 & 9 & 6.8 & 4 \\14 & 5 & 8 & 8 & 7 & 6 & 6.8 & 3 \\15 & 7 & 12 & 10 & 6 & 10 & 9.0 & 6 \\16 & 7 & 11 & 4 & 7 & 8 & 7.4 & 7 \\17 & 8 & 4 & 5 & 4 & 7 & 5.6 & 4 \\18 & 11 & 4 & 11 & 11 & 10 & 9.4 & 7 \\19 & 6 & 10 & 6 & 10 & 10 & 8.4 & 4 \\20 & 6 & 12 & 12 & 6 & 8 & 8.8 & 6\end{array}\end{array}$$ She also decides that the upper specification limit is 10 blemishes.

-Referring to Scenario 18-7, based on the $\bar { X }$ chart for the number of blemishes, it
appears that the process is out of control.

Question 62

SCENARIO 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. She also decides that the upper specification limit is 10 blemishes.
Referring to Scenario 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 mean of the sample ranges by D4. For
this data set, the value of D4 is ________.

Question 63

SCENARIO 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 follow.
Referring to Scenario 18-6, a p control chart is to be constructed for these data. The estimate of
the standard error of the sample proportion is __________.

Question 64

SCENARIO 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. She also decides that the upper specification limit is 10 blemishes.
Referring to Scenario 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 mean of the sample ranges by D3. For
this data set, the value of D3 is ________.

Question 65

SCENARIO 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 follow.
Referring to Scenario 18-6, a p control chart is to be constructed for these data. The lower control
limit is __________, while the upper control limit is __________.

Question 66

SCENARIO 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. She also decides that the upper specification limit is 10 blemishes.
Referring to Scenario 18-7, an R chart is to be constructed for the number of blemishes. The
lower control limit for this data set is ________.

Question 67

SCENARIO 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. She also decides that the upper specification limit is 10 blemishes.
Referring to Scenario 18-7, an 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 68

SCENARIO 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. $$\begin{array}{l}\text {\quad\quad\quad\quad\quad\quad\quad Sheet }\\\begin{array} { r r r r r r r r } \underline {\text { Day } }& \underline { 1 } &\underline { 2 }&\underline { 3 }& \underline {4 }& \underline {5} & \underline { \text { Mean } } &\underline { \text { Range }} \\1 & 8 & 10 & 14 & 6 & 5 & 8.6 & 9 \\2 & 8 & 13 & 6 & 6 & 10 & 8.6 & 7 \\3 & 10 & 12 & 7 & 7 & 9 & 9.0 & 5 \\4 & 5 & 9 & 12 & 7 & 10 & 8.6 & 7 \\5 & 8 & 3 & 8 & 9 & 10 & 7.6 & 7 \\6 & 9 & 7 & 9 & 6 & 9 & 8.0 & 3 \\7 & 10 & 10 & 5 & 7 & 6 & 7.6 & 5 \\8 & 10 & 9 & 10 & 6 & 5 & 8.0 & 5 \\9 & 6 & 10 & 6 & 9 & 9 & 8.0 & 4 \\10 & 6 & 9 & 8 & 6 & 8 & 7.4 & 3 \\11 & 8 & 5 & 6 & 10 & 10 & 7.8 & 5 \\12 & 6 & 4 & 7 & 7 & 12 & 7.2 & 8 \\13 & 7 & 5 & 7 & 6 & 9 & 6.8 & 4 \\14 & 5 & 8 & 8 & 7 & 6 & 6.8 & 3 \\15 & 7 & 12 & 10 & 6 & 10 & 9.0 & 6 \\16 & 7 & 11 & 4 & 7 & 8 & 7.4 & 7 \\17 & 8 & 4 & 5 & 4 & 7 & 5.6 & 4 \\18 & 11 & 4 & 11 & 11 & 10 & 9.4 & 7 \\19 & 6 & 10 & 6 & 10 & 10 & 8.4 & 4 \\20 & 6 & 12 & 12 & 6 & 8 & 8.8 & 6\end{array}\end{array}$$ She also decides that the upper specification limit is 10 blemishes.

-Referring to Scenario 18-7, based on the R chart, it appears that the process is out
of control.

Question 69

SCENARIO 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. She also decides that the upper specification limit is 10 blemishes.
Referring to Scenario 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 70

SCENARIO 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 follow.
Referring to Scenario 18-6, construct a p control chart for these data.

Question 71

SCENARIO 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. She also decides that the upper specification limit is 10 blemishes.
Referring to Scenario 18-7, construct an R chart for the number of blemishes.

Question 72

SCENARIO 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. She also decides that the upper specification limit is 10 blemishes.
Referring to Scenario 18-7, an chart is to be used for the number of blemishes. The center line
of this chart is located at __________.

Question 73

SCENARIO 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. She also decides that the upper specification limit is 10 blemishes.
Referring to Scenario 18-7, what percentage of the chips will fall below the upper specification
limit?

Question 74

SCENARIO 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. She also decides that the upper specification limit is 10 blemishes.
Referring to Scenario 18-7, construct an chart for the number of blemishes.

Question 75

SCENARIO 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. She also decides that the upper specification limit is 10 blemishes.
Referring to Scenario 18-7, what is the value of factor?

Question 76

SCENARIO 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. She also decides that the upper specification limit is 10 blemishes.
Referring to Scenario 18-7, what is the value of the CPU index?

Question 77

SCENARIO 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. She also decides that the upper specification limit is 10 blemishes.
Referring to Scenario 18-7, an 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 mean of the sample ranges. For this data set, the value of A2 is ________.

Question 78

SCENARIO 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. She also decides that the upper specification limit is 10 blemishes.
Referring to Scenario 18-7, an R chart is to be constructed for the number of blemishes. The
upper control limit for this data set is ________.

Question 79

SCENARIO 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.
Referring to Scenario 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 80

SCENARIO 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 follow. $$\begin{array} { r c c } \underline {\text { Day }} & \begin{array} { c } \text { Number } \\\underline {\text { Poor }}\end{array} & \begin{array} { c } \text { Proportion } \\\underline {\text { Poor }}\end{array} \\1 & 33 & 0.0550000 \\2 & 29 & 0.0483333 \\3 & 31 & 0.0516667 \\4 & 32 & 0.0533333 \\5 & 43 & 0.0716667 \\6 & 45 & 0.0750000 \\7 & 46 & 0.0766667 \\8 & 48 & 0.0800000 \\9 & 48 & 0.0800000 \\10 & 46 & 0.0766667 \\11 & 28 & 0.0466667 \\12 & 32 & 0.0533333 \\13 & 28 & 0.0466667 \\14 & 32 & 0.0533333 \\15 & 31 & 0.0516667 \\16 & 24 & 0.0400000\end{array}$$

-Referring to Scenario 18-6, the process seems to be in control.