Deck 13: Methods for Quality Improvement: Statistical Process Control Available on CD

Question 1

Does the following control chart represent a process that is in control or out of control? If it
is out of control, explain how you arrived at this conclusion.

Answer 1

in control

Question 2

Does the following control chart represent a process that is in control or out of control? If it is out of control, explain how you arrived at this conclusion.

Answer 2

in control

Question 3

(Situation E) A machine at K-Company fills boxes with bran flake cereal. The target weight for the filled boxes is 24 ounces. The company would like to use control charts to monitor the performance of the machine. The company decides to sample and weigh 10 consecutive boxes of cereal at randomly selected times over a two-week period. Twenty measurement times are selected and the following information is recorded. $$\begin{array} { c c c c c c } \hline \text { Time } & \text { Mean (oz) } & \text { Range (oz) } & \text { Time } & \text { Mean (oz) } & \text { Range (oz) } \\\hline 1 & 23.8 & 1.05 & 11 & 24.5 & 1.21 \\2 & 24.5 & 0.85 & 12 & 24.7 & 0.65 \\3 & 23.9 & 1.12 & 13 & 24.0 & 0.55 \\4 & 24.2 & 0.95 & 14 & 25.5 & 3.21 \\5 & 23.7 & 1.22 & 15 & 24.2 & 1.25 \\6 & 23.5 & 1.42 & 16 & 24.4 & 1.35 \\7 & 24.2 & 1.02 & 17 & 24.5 & 0.98 \\8 & 24.4 & 1.10 & 18 & 25.0 & 1.30 \\9 & 24.1 & 0.75 & 19 & 24.1 & 0.88 \\10 & 24.2 & 0.60 & 20 & 24.2 & 1.01 \\\hline\end{array}$$

-Find the upper and lower control limits for the R-chart.

Answer 3

Upper Control Limit $= \bar { R } D _ { 4 } = 1.1235 ( 1.777 ) = 1.996$
Lower Control Limit $= \bar { R } D _ { 3 } = 1.1235 ( 0.223 ) = 0.251$

Question 4

_______ are boundary points that define the acceptable values for an output variable.

A) Control bounds
B) Tolerance limits
C) Capability limits
D) Specification limits

Question 5

(Situation D) A walk-in freezer thermostat at a restaurant is set at 5°F. Because of the perishability of the food in the freezer, the restaurant manager has decided to begin monitoring the temperature inside the freezer. The managers used a precision thermometer to take sample temperature readings at five randomly chosen times per day for 10 days. The data are presented below.

$\text { Day }$ $\quad$ $\quad$ $\text { Temperature }\left(^{\circ}\right. \text { F) }$
$\begin{array}{rrrrrr}\hline 1 & 5.22 & 5.29 & 5.11 & 4.95 & 4.78 \\2 & 4.40 & 4.41 & 4.63 & 6.03 & 4.83 \\3 & 5.11 & 5.43 & 4.90 & 4.55 & 5.23 \\4 & 5.65 & 4.24 & 5.09 & 4.82 & 5.50 \\5 & 4.68 & 5.92 & 4.71 & 4.67 & 4.75 \\6 & 5.01 & 5.26 & 6.10 & 5.20 & 5.25 \\7 & 5.20 & 4.99 & 5.15 & 5.96 & 5.35 \\8 & 4.30 & 4.91 & 5.03 & 4.97 & 4.80 \\9 & 5.45 & 5.62 & 6.11 & 5.13 & 4.90 \\10 & 5.06 & 5.13 & 4.95 & 5.59 & 5.80 \\\hline\end{array}$


-Calculate the centerline of the R-chart.

Question 6

The table below shows the data from samples of size $n=5$ randomly chosen from the outputs of a process on 20 different days.
$\begin{array}{cccccc}\hline \text { Sample } & & & \text { Data } & & \\\hline 1 & 4.5 & 2.1 & 5.4 & 2.7 & 4.5 \\2 & 3.6 & 3.5 & 6.1 & 4.9 & 4.2 \\3 & 5.1 & 6.2 & 2.4 & 3.7 & 5.1 \\4 & 4.9 & 5.4 & 3.5 & 5.4 & 3.7 \\5 & 4.1 & 3.8 & 3.8 & 4.6 & 4.9 \\6 & 3.7 & 4.6 & 4.8 & 4.2 & 5.2 \\7 & 5.6 & 4.7 & 4.1 & 5.1 & 3.1 \\8 & 4.8 & 5.1 & 4.3 & 4.6 & 2.7 \\9 & 6.1 & 4.6 & 4.7 & 3.8 & 4.2 \\10 & 2.4 & 4.8 & 5.6 & 4.1 & 4.8 \\11 & 3.7 & 5.3 & 2.9 & 4.7 & 6.3 \\12 & 4.5 & 3.4 & 3.4 & 5.2 & 4.5 \\13 & 5.2 & 2.7 & 5.1 & 6.2 & 2.9 \\14 & 3.4 & 5.5 & 4.6 & 2.4 & 3.4 \\15 & 4.8 & 3.6 & 4.8 & 4.4 & 4.6 \\16 & 4.1 & 4.6 & 4.9 & 4.9 & 4.3 \\17 & 4.6 & 3.7 & 3.5 & 3.7 & 5.2 \\18 & 5.1 & 4.2 & 5.6 & 4.1 & 5.7 \\19 & 3.7 & 4.8 & 4.9 & 2.3 & 4.5 \\20 & 5.4 & 3.9 & 4.2 & 5.4 & 4.3 \\\hline\end{array}$

a. $\text { Find } D_{3} \text { and } D_{4} \text {. }$
b. $\text { Construct an R-chart. }$
c. $\text { Is the process out of control? Explain. }$

Question 7

Does the following control chart represent a process that is in control or out of control? If it is out of control, explain how you arrived at this conclusion.

Question 8

Does the following control chart represent a process that is in control or out of control? If it is out of control, explain how you arrived at this conclusion.

Question 9

(Situation E) A machine at K-Company fills boxes with bran flake cereal. The target weight for the filled boxes is 24
ounces. The company would like to use control charts to monitor the performance of the machine. The company decides
to sample and weigh 10 consecutive boxes of cereal at randomly selected times over a two-week period. Twenty
measurement times are selected and the following information is recorded.
Calculate the centerline for constructing the

Question 10

The table below shows the data from samples of size $n=5$ randomly chosen from the outputs of a process on 20 different days. Assume the specification limits are USL $=2.1$ and $\mathrm{LSL}=5.7$ .


$\begin{array}{cccccc}\hline \text { Sample } & & {\text { Data }} \\\hline 1 & 4.5 & 2.1 & 5.4 & 2.7 & 4.5 \\2 & 3.6 & 3.5 & 6.1 & 4.9 & 4.2 \\3 & 5.1 & 6.2 & 2.4 & 3.7 & 5.1 \\4 & 4.9 & 5.4 & 3.5 & 5.4 & 3.7 \\5 & 4.1 & 3.8 & 3.8 & 4.6 & 4.9 \\6 & 3.7 & 4.6 & 4.8 & 4.2 & 5.2 \\7 & 5.6 & 4.7 & 4.1 & 5.1 & 3.1 \\8 & 4.8 & 5.1 & 4.3 & 4.6 & 2.7 \\9 & 6.1 & 4.6 & 4.7 & 3.8 & 4.2 \\10 & 2.4 & 4.8 & 5.6 & 4.1 & 4.8 \\11 & 3.7 & 5.3 & 2.9 & 4.7 & 6.3 \\12 & 4.5 & 3.4 & 3.4 & 5.2 & 4.5 \\13 & 5.2 & 2.7 & 5.1 & 6.2 & 2.9 \\14 & 3.4 & 5.5 & 4.6 & 2.4 & 3.4 \\15 & 4.8 & 3.6 & 4.8 & 4.4 & 4.6 \\16 & 4.1 & 4.6 & 4.9 & 4.9 & 4.3 \\17 & 4.6 & 3.7 & 3.5 & 3.7 & 5.2 \\18 & 5.1 & 4.2 & 5.6 & 4.1 & 5.7 \\19 & 3.7 & 4.8 & 4.9 & 2.3 & 4.5 \\20 & 5.4 & 3.9 & 4.2 & 5.4 & 4.3 \\\hline\end{array}$
a. Assuming the process is under control, construct a capability analysis diagram for the process.
b. Find the percentage of data items that fall outside the specification limits.
c. Is the process capable? Support your answer with a numerical measure of capability.

Question 11

(Situation E) A machine at K-Company fills boxes with bran flake cereal. The target weight for the filled boxes is 24 ounces. The company would like to use control charts to monitor the performance of the machine. The company decides to sample and weigh 10 consecutive boxes of cereal at randomly selected times over a two-week period. Twenty measurement times are selected and the following information is recorded. $$\begin{array} { c c c c c c } \hline \text { Time } & \text { Mean (oz) } & \text { Range (oz) } & \text { Time } & \text { Mean (oz) } & \text { Range (oz) } \\\hline 1 & 23.8 & 1.05 & 11 & 24.5 & 1.21 \\2 & 24.5 & 0.85 & 12 & 24.7 & 0.65 \\3 & 23.9 & 1.12 & 13 & 24.0 & 0.55 \\4 & 24.2 & 0.95 & 14 & 25.5 & 3.21 \\5 & 23.7 & 1.22 & 15 & 24.2 & 1.25 \\6 & 23.5 & 1.42 & 16 & 24.4 & 1.35 \\7 & 24.2 & 1.02 & 17 & 24.5 & 0.98 \\8 & 24.4 & 1.10 & 18 & 25.0 & 1.30 \\9 & 24.1 & 0.75 & 19 & 24.1 & 0.88 \\10 & 24.2 & 0.60 & 20 & 24.2 & 1.01\end{array}$$

- $$\text { Create the } \bar { x } \text {-chart and interpret it. }$$

Question 12

The upper and lower control limits are usually a distance of _______ from the centerline.

A) 3 standard deviations
B) 1 standard deviation
C) 2 standard deviations
D) 3.5 standard deviations

Question 13

The process of monitoring and eliminating variation in order to keep a process in a state of control or to bring a process into control is called

A) a process distribution.
B) random behavior.
C) statistical process control.
D) a control chart.

Question 14

(Situation B) A manufacturing company makes hemostats for hospital emergency rooms. The company is interested in implementing statistical process control procedures in its production operation. The production manager believes that the proportion of defective hemostats generated by the process is about 3%. The company collected one sample of 300 consecutively manufactured hemostats each day for 20 days.
The data are shown below.
$$\begin{array} { c c c c c c } \hline \text { Sample } & \text { Sample Size } & \text { Defectives } & \text { Sample } & \text { Sample Size } & \text { Defectives } \\\hline 1 & 300 & 8 & 11 & 300 & 12 \\2 & 300 & 6 & 12 & 300 & 11 \\3 & 300 & 11 & 13 & 300 & 14 \\4 & 300 & 15 & 14 & 300 & 8 \\5 & 300 & 12 & 15 & 300 & 7 \\6 & 300 & 11 & 16 & 300 & 3 \\7 & 300 & 9 & 17 & 300 & 9 \\8 & 300 & 6 & 18 & 300 & 11 \\9 & 300 & 5 & 19 & 300 & 10 \\10 & 300 & 4 & 20 & 300 & 6 \\\hline\end{array}$$

-Construct the p-chart and interpret it.

Question 15

The capability index for a process centered on the desired mean is

A) $C _ { p } = \frac { ( U S L - L S L ) } { 6 \sigma }$

B) $C _ { p } = \frac { 3 \sigma } { ( U S L - L S L ) }$

C) $C _ { p } = \frac { 6 \sigma } { ( U S L - L S L ) }$

D) $C _ { p } = \frac { ( U S L - L S L ) } { 3 \sigma }$

Question 16

Does the following control chart represent a process that is in control or out of control? If it is out of control, explain how you arrived at this conclusion.

Question 17

(Situation E) A machine at K-Company fills boxes with bran flake cereal. The target weight for the filled boxes is 24 ounces. The company would like to use control charts to monitor the performance of the machine. The company decides to sample and weigh 10 consecutive boxes of cereal at randomly selected times over a two-week period. Twenty measurement times are selected and the following information is recorded. $$\begin{array} { c c c c c c } \hline \text { Time } & \text { Mean (oz) } & \text { Range (oz) } & \text { Time } & \text { Mean (oz) } & \text { Range (oz) } \\\hline 1 & 23.8 & 1.05 & 11 & 24.5 & 1.21 \\2 & 24.5 & 0.85 & 12 & 24.7 & 0.65 \\3 & 23.9 & 1.12 & 13 & 24.0 & 0.55 \\4 & 24.2 & 0.95 & 14 & 25.5 & 3.21 \\5 & 23.7 & 1.22 & 15 & 24.2 & 1.25 \\6 & 23.5 & 1.42 & 16 & 24.4 & 1.35 \\7 & 24.2 & 1.02 & 17 & 24.5 & 0.98 \\8 & 24.4 & 1.10 & 18 & 25.0 & 1.30 \\9 & 24.1 & 0.75 & 19 & 24.1 & 0.88 \\10 & 24.2 & 0.60 & 20 & 24.2 & 1.01\end{array}$$

-Does the following control chart represent a process that is in control or out of control? If it is out of control, explain how you arrived at this conclusion.

Question 18

The primary goal of quality-improvement activities is

A) to reduce variation.
B) to increase the mean.
C) to increase variation.
D) to change the process.

Question 19

A process is considered capable if

A) $\mathrm { C } _ { \mathrm { p } } > 1$
B) $\mathrm { C } _ { \mathrm { p } } \leq 1$ .
C) $\mathrm { C } _ { \mathrm { p } } \geq 1$ .
D) $\mathrm { C } _ { \mathrm { p } } < 1$ .

Question 20

(Situation D) A walk-in freezer thermostat at a restaurant is set at 5°F. Because of the perishability of the food in the freezer, the restaurant manager has decided to begin monitoring the temperature inside the freezer. The managers used a precision thermometer to take sample temperature readings at five randomly chosen times per day for 10 days. The data are presented below.

$\text { Day }$ $\quad$ $\quad$ $\text { Temperature }\left(^{\circ}\right. \text { F) }$
$\begin{array}{rrrrrr}\hline 1 & 5.22 & 5.29 & 5.11 & 4.95 & 4.78 \\2 & 4.40 & 4.41 & 4.63 & 6.03 & 4.83 \\3 & 5.11 & 5.43 & 4.90 & 4.55 & 5.23 \\4 & 5.65 & 4.24 & 5.09 & 4.82 & 5.50 \\5 & 4.68 & 5.92 & 4.71 & 4.67 & 4.75 \\6 & 5.01 & 5.26 & 6.10 & 5.20 & 5.25 \\7 & 5.20 & 4.99 & 5.15 & 5.96 & 5.35 \\8 & 4.30 & 4.91 & 5.03 & 4.97 & 4.80 \\9 & 5.45 & 5.62 & 6.11 & 5.13 & 4.90 \\10 & 5.06 & 5.13 & 4.95 & 5.59 & 5.80 \\\hline\end{array}$


-Calculate the upper and lower control limits for the R-chart.

Question 21

The quality of a product is indicated by the extent to which it satisfies the needs and preferences of its manufacturer.

Question 22

(Situation C) Ten samples of $n = 5$ were collected to construct an $\bar { x }$ -chart. The sample means and ranges for the 10 samples are shown below.


$\begin{array}{cccccc}\hline \text { Sample } & \text { Mean } & \text { Range } & \text { Sample } & \text { Mean } & \text { Range } \\\hline 1 & 20.2 & 2.7 & 6 & 20.4 & 1.9 \\2 & 22.4 & 1.8 & 7 & 15.9 & 1.0 \\3 & 21.2 & 1.5 & 8 & 22.3 & 2.1 \\4 & 18.2 & 1.2 & 9 & 20.7 & 1.6 \\5 & 23.2 & 2.4 & 10 & 21.1 & 1.8 \\\hline\end{array}$


-Calculate the upper and lower control limits for the $\bar { X } \text {-chart. }$

Question 23

With rare exceptions, all items produced by a process are identical.

Question 24

Question 25

Does the following control chart represent a process that is in control or out of control? If it is out of control, explain how you arrived at this conclusion.

Question 26

(Situation E) A machine at K-Company fills boxes with bran flake cereal. The target weight for the filled boxes is 24 ounces. The company would like to use control charts to monitor the performance of the machine. The company decides to sample and weigh 10 consecutive boxes of cereal at randomly selected times over a two-week period. Twenty measurement times are selected and the following information is recorded. $$\begin{array} { c c c c c c } \hline \text { Time } & \text { Mean (oz) } & \text { Range (oz) } & \text { Time } & \text { Mean (oz) } & \text { Range (oz) } \\\hline 1 & 23.8 & 1.05 & 11 & 24.5 & 1.21 \\2 & 24.5 & 0.85 & 12 & 24.7 & 0.65 \\3 & 23.9 & 1.12 & 13 & 24.0 & 0.55 \\4 & 24.2 & 0.95 & 14 & 25.5 & 3.21 \\5 & 23.7 & 1.22 & 15 & 24.2 & 1.25 \\6 & 23.5 & 1.42 & 16 & 24.4 & 1.35 \\7 & 24.2 & 1.02 & 17 & 24.5 & 0.98 \\8 & 24.4 & 1.10 & 18 & 25.0 & 1.30 \\9 & 24.1 & 0.75 & 19 & 24.1 & 0.88 \\10 & 24.2 & 0.60 & 20 & 24.2 & 1.01\end{array}$$

-Calculate the upper and lower control limits for the $\bar { x } \text {-chart. }$

Question 27

(Situation E) A machine at K-Company fills boxes with bran flake cereal. The target weight for the filled boxes is 24 ounces. The company would like to use control charts to monitor the performance of the machine. The company decides to sample and weigh 10 consecutive boxes of cereal at randomly selected times over a two-week period. Twenty measurement times are selected and the following information is recorded. $$\begin{array} { c c c c c c } \hline \text { Time } & \text { Mean (oz) } & \text { Range (oz) } & \text { Time } & \text { Mean (oz) } & \text { Range (oz) } \\\hline 1 & 23.8 & 1.05 & 11 & 24.5 & 1.21 \\2 & 24.5 & 0.85 & 12 & 24.7 & 0.65 \\3 & 23.9 & 1.12 & 13 & 24.0 & 0.55 \\4 & 24.2 & 0.95 & 14 & 25.5 & 3.21 \\5 & 23.7 & 1.22 & 15 & 24.2 & 1.25 \\6 & 23.5 & 1.42 & 16 & 24.4 & 1.35 \\7 & 24.2 & 1.02 & 17 & 24.5 & 0.98 \\8 & 24.4 & 1.10 & 18 & 25.0 & 1.30 \\9 & 24.1 & 0.75 & 19 & 24.1 & 0.88 \\10 & 24.2 & 0.60 & 20 & 24.2 & 1.01\end{array}$$

-Calculate the centerline of the $\mathrm { R } - \text { chart }$

Question 28

Does the following control chart represent a process that is in control or out of control? If it is out of control, explain how you arrived at this conclusion.

Question 29

(Situation B) A manufacturing company makes hemostats for hospital emergency rooms. The company is interested in implementing statistical process control procedures in its production operation. The production manager believes that the proportion of defective hemostats generated by the process is about 3%. The company collected one sample of 300 consecutively manufactured hemostats each day for 20 days. The data are shown below. $$\begin{array} { c c c c c c } \hline \text { Sample } & \text { Sample Size } & \text { Defectives } & \text { Sample } & \text { Sample Size } & \text { Defectives } \\\hline 1 & 300 & 8 & 11 & 300 & 12 \\2 & 300 & 6 & 12 & 300 & 11 \\3 & 300 & 11 & 13 & 300 & 14 \\4 & 300 & 15 & 14 & 300 & 8 \\5 & 300 & 12 & 15 & 300 & 7 \\6 & 300 & 11 & 16 & 300 & 3 \\7 & 300 & 9 & 17 & 300 & 9 \\8 & 300 & 6 & 18 & 300 & 11 \\9 & 300 & 5 & 19 & 300 & 10 \\10 & 300 & 4 & 20 & 300 & 6 \\\hline\end{array}$$

-Find the upper and lower control limits for the p-chart.

Question 30

(Situation D) A walk-in freezer thermostat at a restaurant is set at 5°F. Because of the perishability of the food in the freezer, the restaurant manager has decided to begin monitoring the temperature inside the freezer. The managers used a precision thermometer to take sample temperature readings at five randomly chosen times per day for 10 days. The data are presented below.

$\text { Day }$ $\quad$ $\quad$ $\text { Temperature }\left(^{\circ}\right. \text { F) }$
$\begin{array}{rrrrrr}\hline 1 & 5.22 & 5.29 & 5.11 & 4.95 & 4.78 \\2 & 4.40 & 4.41 & 4.63 & 6.03 & 4.83 \\3 & 5.11 & 5.43 & 4.90 & 4.55 & 5.23 \\4 & 5.65 & 4.24 & 5.09 & 4.82 & 5.50 \\5 & 4.68 & 5.92 & 4.71 & 4.67 & 4.75 \\6 & 5.01 & 5.26 & 6.10 & 5.20 & 5.25 \\7 & 5.20 & 4.99 & 5.15 & 5.96 & 5.35 \\8 & 4.30 & 4.91 & 5.03 & 4.97 & 4.80 \\9 & 5.45 & 5.62 & 6.11 & 5.13 & 4.90 \\10 & 5.06 & 5.13 & 4.95 & 5.59 & 5.80 \\\hline\end{array}$


-Create the R-chart and interpret it.

Question 31

Question 32

If all points fall between the control limits, then we may safely conclude that the process is in statistical control.

Question 33

Control charts are used to help us differentiate between process variation due to common causes and special causes.

Question 34

(Situation C) Ten samples of $n = 5$ were collected to construct an $\bar { x }$ -chart. The sample means and ranges for the 10 samples are shown below.


$\begin{array}{cccccc}\hline \text { Sample } & \text { Mean } & \text { Range } & \text { Sample } & \text { Mean } & \text { Range } \\\hline 1 & 20.2 & 2.7 & 6 & 20.4 & 1.9 \\2 & 22.4 & 1.8 & 7 & 15.9 & 1.0 \\3 & 21.2 & 1.5 & 8 & 22.3 & 2.1 \\4 & 18.2 & 1.2 & 9 & 20.7 & 1.6 \\5 & 23.2 & 2.4 & 10 & 21.1 & 1.8 \\\hline\end{array}$


-Calculate the centerline for constructing the $\bar { x } \text {-chart. }$

Question 35

The R-chart is used to detect changes in process variation.

Question 36

The centerline of a control chart is drawn at the level of the median of the sample.

Question 37

People, machines, and raw materials can all contribute to the variability in the output of a system.

Question 38

Question 39

When n ≤ 6, the R-chart contains only one control limit, the lower control limit.

Question 40

The table below shows the data from samples of size $n=5$ randomly chosen from the outputs of a process on 20 different days.

$\begin{array}{cccccc}\hline \text { Sample } & & {\text { Data }} \\\hline 1 & 4.5 & 2.1 & 5.4 & 2.7 & 4.5 \\2 & 3.6 & 3.5 & 6.1 & 4.9 & 4.2 \\3 & 5.1 & 6.2 & 2.4 & 3.7 & 5.1 \\4 & 4.9 & 5.4 & 3.5 & 5.4 & 3.7 \\5 & 4.1 & 3.8 & 3.8 & 4.6 & 4.9 \\6 & 3.7 & 4.6 & 4.8 & 4.2 & 5.2 \\7 & 5.6 & 4.7 & 4.1 & 5.1 & 3.1 \\8 & 4.8 & 5.1 & 4.3 & 4.6 & 2.7 \\9 & 6.1 & 4.6 & 4.7 & 3.8 & 4.2 \\10 & 2.4 & 4.8 & 5.6 & 4.1 & 4.8 \\11 & 3.7 & 5.3 & 2.9 & 4.7 & 6.3 \\12 & 4.5 & 3.4 & 3.4 & 5.2 & 4.5 \\13 & 5.2 & 2.7 & 5.1 & 6.2 & 2.9 \\14 & 3.4 & 5.5 & 4.6 & 2.4 & 3.4 \\15 & 4.8 & 3.6 & 4.8 & 4.4 & 4.6 \\16 & 4.1 & 4.6 & 4.9 & 4.9 & 4.3 \\17 & 4.6 & 3.7 & 3.5 & 3.7 & 5.2 \\18 & 5.1 & 4.2 & 5.6 & 4.1 & 5.7 \\19 & 3.7 & 4.8 & 4.9 & 2.3 & 4.5 \\20 & 5.4 & 3.9 & 4.2 & 5.4 & 4.3 \\\hline\end{array}$

a. $\text { Calculate } \bar{x} \text {. }$
b. $\text { Calculate } \bar{R} \text {. }$
c. $\text { Find } d_{2} \text { and } A_{2} \text {. }$
d. $\text { Construct an } \bar{x} \text {-chart. }$
e. $\text { Is the process out of control? Explain. }$

Question 41

When using a cause-and-effect diagram in process diagnosis, you begin by specifying the cause of interest and then move forward to identify potential effects of this cause.

Question 42

The elimination of common causes of variation is typically the responsibility of workers, not management.

Question 43

The p-chart is based on the assumption that the number of defective units in each sample is a binomial random variable.

Question 44

The variation in the output of processes that are out of control can be entirely attributed to random behavior.

Question 45

The distribution that describes the output variable of a process may change over time.

Question 46

Statistical process control consists of monitoring process variation, diagnosing causes of variation, and eliminating those causes.

Question 47

A process may be in control but still not be capable of producing output that is acceptable to customers.

Question 48

A process is in control and has a normally distributed output distribution with mean of 1000 and a standard deviation of 100 . The upper and lower specification limits for the process are 1060 and 940 , respectively. Find the $\mathrm { C } _ { \mathrm { p } }$ value of the process. Is the system capable?

A) $\mathrm { C } _ { \mathrm { p } } = 0.2$ ; the system is capable.
B) $\mathrm { C } _ { \mathrm { p } } = 3.333$ ; the system is not capable.
C) $C _ { p } = 3.333$ ; the system is capable.
D) $\mathrm { C } _ { \mathrm { p } } = 0.2$ ; the system is not capable.

Question 49

Find the process spread when

A) 39
B) 156
C) 26
D) 78

Question 50

If the R-chart indicates that the process variation is in control, then it makes sense to construct and interpret the $\overline { \mathrm { X } }$ chart.

Question 51

An in-control, centered process that follows a normal distribution has a of 3.0. How many standard deviations away from the process mean is the upper specification limit?

A) 9
B) 3
C) 18
D) 6

Question 52

An unbiased estimator for ? can be found by dividing the mean of the ranges, $\overline { \mathrm { R } }$ by an appropriate constant.

Question 53

Conformance refers to the extent to which a good or service can be adapted for use in new situations.

Question 54

Estimate the process spread when s

A) 0.0096
B) 0.0064
C) 0.0384
D) 0.0192

Question 55

In constructing a p-chart, it is advisable to use a much smaller sample size than is typically used for $\bar { x } -$ and R-charts.

Question 56

The diagnosis phase of statistical process control is concerned with tracking down causes of variation.

Question 57

When constructing an $\bar { x }$ -chart, $\bar{\bar { x }}$ is used as the estimator of $\mu$ .

Question 58

Performance, reliability, and durability are some of the factors used to evaluate quality.

Question 59

A process adds value to the inputs of the process.

Question 60

(Situation B) A manufacturing company makes hemostats for hospital emergency rooms. The company is interested in implementing statistical process control procedures in its production operation. The production manager believes that the proportion of defective hemostats generated by the process is about 3%. The company collected one sample of 300
consecutively manufactured hemostats each day for 20 days. The data are shown below. $$\begin{array} { c c c c c c } \hline \text { Sample } & \text { Sample Size } & \text { Defectives } & \text { Sample } & \text { Sample Size } & \text { Defectives } \\\hline 1 & 300 & 8 & 11 & 300 & 12 \\2 & 300 & 6 & 12 & 300 & 11 \\3 & 300 & 11 & 13 & 300 & 14 \\4 & 300 & 15 & 14 & 300 & 8 \\5 & 300 & 12 & 15 & 300 & 7 \\6 & 300 & 11 & 16 & 300 & 3 \\7 & 300 & 9 & 17 & 300 & 9 \\8 & 300 & 6 & 18 & 300 & 11 \\9 & 300 & 5 & 19 & 300 & 10 \\10 & 300 & 4 & 20 & 300 & 6 \\\hline\end{array}$$

-Calculate the centerline used in constructing a $\mathrm { p } \text {-chart. }$

A) .0317
B) .0297
C) .0593
D) .0245

Question 61

Capability analysis is used to determine when process variation is unacceptably high.

Question 62

A) 0.3333
B) 18
C) 3
D) 0.0556

Question 63

(Situation D) A walk-in freezer thermostat at a restaurant is set at 5°F. Because of the perishability of the food in the freezer, the restaurant manager has decided to begin monitoring the temperature inside the freezer. The managers used a precision thermometer to take sample temperature readings at five randomly chosen times per day for 10 days. The data
are presented below.

$\text { Day }$ $\quad$ $\quad$ $\text { Temperature }\left(^{\circ}\right. \text { F) }$
$\begin{array}{cccccc}\hline 1 & 5.22 & 5.29 & 5.11 & 4.95 & 4.78 \\2 & 4.40 & 4.41 & 4.63 & 6.03 & 4.83 \\3 & 5.11 & 5.43 & 4.90 & 4.55 & 5.23 \\4 & 5.65 & 4.24 & 5.09 & 4.82 & 5.50 \\5 & 4.68 & 5.92 & 4.71 & 4.67 & 4.75 \\6 & 5.01 & 5.26 & 6.10 & 5.20 & 5.25 \\7 & 5.20 & 4.99 & 5.15 & 5.96 & 5.35 \\8 & 4.30 & 4.91 & 5.03 & 4.97 & 4.80 \\9 & 5.45 & 5.62 & 6.11 & 5.13 & 4.90 \\10 & 5.06 & 5.13 & 4.95 & 5.59 & 5.80 \\\hline\end{array}$

-Calculate the centerline for constructing the $\bar { x }$ chart.

A) 5.3062
B) 10.245
C) 5.1224
D) 5.0700

Question 64

Estimate the process spread when s

A) 321.24
B) 214.16
C) 1284.96
D) 642.48

Question 65

A) 0.375
B) 4.5
C) 0.75
D) 1.5

Question 66

Most processes are naturally in a state of statistical control.

Question 67

(Situation A) To construct a p-chart for a manufacturing process, 20 samples of size 100 were selected. The results are shown below: $$\begin{array} { c c c c c c } \hline \text { Sample } & \text { Sample Size } & \text { Defectives } & \text { Sample } & \text { Sample Size } & \text { Defectives } \\\hline 1 & 100 & 10 & 11 & 100 & 8 \\2 & 100 & 8 & 12 & 100 & 8 \\3 & 100 & 9 & 13 & 100 & 5 \\4 & 100 & 6 & 14 & 100 & 9 \\5 & 100 & 7 & 15 & 100 & 7 \\6 & 100 & 3 & 16 & 100 & 9 \\7 & 100 & 8 & 17 & 100 & 11 \\8 & 100 & 6 & 18 & 100 & 4 \\9 & 100 & 11 & 19 & 100 & 6 \\10 & 100 & 10 & 20 & 100 & 8 \\\hline\end{array}$$

-Calculate the upper and lower control limits for the p-chart.

A) $\bar { p } \pm .1783$
B) $\bar { p } \pm .0797$
C) $\bar { p } \pm .0532$
D) $\bar { p } \pm .0266$

Question 68

The p-chart is typically used to monitor the proportion of units that conform to specification.

Question 69

Special causes of variation can often be diagnosed and eliminated by workers or their immediate supervisors.

Question 70

Find the specification spread when USL

A) 0.77
B) 1.67
C) 2
D) 0.67

Question 71

Control charts are the tool of choice for continuously monitoring processes.

Question 72

A business that operates out-of-control processes risks losing its customers and threatens its own survival.

Question 73

Control charts may only be used for quantitative quality variables.

Question 74

A system receives inputs from its environment, transforms those inputs to outputs, and delivers them to its environment.

Question 75

(Situation A) To construct a p-chart for a manufacturing process, 20 samples of size 100 were selected. The results areshown below:

$$\begin{array} { c c c c c c } \hline \text { Sample } & \text { Sample Size } & \text { Defectives } & \text { Sample } & \text { Sample Size } & \text { Defectives } \\\hline 1 & 100 & 10 & 11 & 100 & 8 \\2 & 100 & 8 & 12 & 100 & 8 \\3 & 100 & 9 & 13 & 100 & 5 \\4 & 100 & 6 & 14 & 100 & 9 \\5 & 100 & 7 & 15 & 100 & 7 \\6 & 100 & 3 & 16 & 100 & 9 \\7 & 100 & 8 & 17 & 100 & 11 \\8 & 100 & 6 & 18 & 100 & 4 \\9 & 100 & 11 & 19 & 100 & 6 \\10 & 100 & 10 & 20 & 100 & 8 \\\hline\end{array}$$

-Calculate the centerline used in constructing a p-chart.

A) .0706
B) .0532
C) .0765
D) .0266

Question 76

The upper and lower control limits are positioned so that when the process is in control the probability of an individual value of the output variable falling outside the control limits is very large.

Question 77

If quality is designed into products and process management is used in their production, massinspection of finished products will not be necessary.

Question 78

If a capability analysis study indicates that an in-control process is not capable, it is usually off-centeredness, rather than variation, that is the culprit.

Question 79

Control limits and specification limits are essentially the same thing.

Question 80

Control charts are useful for evaluating the past performance of a process, for monitoring its current performance, and for predicting future performance.