Question 1

A machine that is supposed to fill small bottles to contain 20 ml yields the following data from a test of 4 bottles every hour. 
$\begin{array}{l|llll|l|l}
S&&&A&&M&R\\hline
1 & 19.9 & 20.1 & 20.2 & 20 . 3& 20.125 & 0.4 \
2 & 20.4 & 20.0 & 20.3 & 20.3 & 20.25 & 0.4 \
3 & 20.0 & 20.7 & 20.4 & 20.3 & 20.35 & 0.7 \
4 & 20.4 & 20.1 & 20.1 & 19.9&20 .125&0 .5\
5 & 19.9 & 19.8 & 19.6 & 19.5 & 19.7 & 0.4 \
6 & 19.4 & 19.4 & 19.6 & 19.7&19 .525&0 .3 \
7 & 19.8 & 19.4 & 19.6 & 19.7&19 .625&0 .4 \
8 & 19.9 & 19.8 & 20.0 & 20.0 & 19.925&0 .2 \
9 & 20.2 & 20.3 & 20.1 & 20.3&20 .225&0 .2\
10 & 20.0 & 20.3 & 20.0 & 20.2 & 20.125&0 .3 \
11 & 20.3 & 20.5 & 20.1 & 20.2&20.275&0 .4 \
12 & 20.1 & 19.9 & 19.8 & 19.7&19 .875&0 .4\
13 & 19.5 & 19.8 & 19.7 & 19.6 & 19.65 & 0.3 \
14 & 19.4 & 19.8 & 19.8 & 19.4 & 19.4 & 0.4 \
15 & 19.5 & 19.6 & 19.6 & 19.9 & 19.65 & 0.4\
\end{array}$

Accepted Answer

The answer of A machine that is supposed to fill...

Question 2

Use the given process data to construct a control chart for p
-A machine that is supposed to produce ball bearings with a diameter of 7 mm yields the following data from a test of 5 ball bearings every 20 minutes.
 $\begin{array} { l|lllll|l|  } S&&&A&&&M&R\
\hline 
1&6.3&6.8&6.9&6.8&6.9&6.74&0.6\2&6.3&6.6&6.6&6.3&7.0&6.56&0.7\
3&6.8&6.7&7.0&6.5&7.0&6.8&0.5\4&7.0&6.7&6.7&6.8&6.8&6.8&0.3\
5&6.8&6.8&6.6&6.5&6.4&6.62&0.4\6&6.8&6.7&6.6&6.3&6.9&6.66&0.6\
7&7.3&7.3&7.4&7.4&7.0&7.28&0.4\8&7.2&7.0&7.2&6.9&7.1&7.08&0.3\
9&7.3&7.6&7.1&7.4&7.6&7.4&0.5\10&7.2&7.6&7.5&7.6&7.1&7.4&0.5\
11&7.2&7.2&7.4&7.0&7.0&7.16&0.4\12&7.5&7.4&7.4&7.6&7.1&7.4&0.5\
\end{array}$

Accepted Answer

The answer of Use the given process data to construct...

Question 3

Use the given process data to construct a control chart for p
-Describe a run chart and give an example. Refer to the values on each of the axes as you describe the run chart.

Accepted Answer

A run chart is a sequential plot of individual data values over time. The horizontal axis typically is used for the time sequence, and the vertical axis is used for the values of the data.

Question 4

A machine is supposed to fill boxes to a weight of 50 lbs. Every 30 minutes a sample of four boxes is tested; the results are given below.
 $$\begin{array} { r | r r r r | r | r } 
\mathrm { S } &&& { \mathrm { A } } && \mathrm { M } & \mathrm { R } \
\hline 1 & 49 & 38 & 39 & 45 & 42.75 & 11 \
2 & 52 & 51 & 43 & 61 & 51.75 & 18 \
3 & 56 & 60 & 32 & 52 & 50 & 28 \
4 & 44 & 59 & 46 & 49 & 49.5 & 15\
5 & 51 & 61 & 48 & 45 & 51.25 & 16 \
6 & 45 & 50 & 46 & 4 8& 47.25 & 5 \
7 & 52 & 51 & 45 & 5 & 50.75 & 10 \
8 & 40 & 50 & 53 & 48&47.75 & 13\
9 & 48 & 67 & 60 & 5 1& 56.5 & 19 \
10 & 43 & 50 & 50 & 47 & 47.5 & 7 \
11 & 48 & 30 & 38 & 39 & 38.75 & 18 \
12 & 50 & 46 & 48 & 53 & 49.25 & 7\
13 & 50 & 58 & 56 & 64 & 57 & 14 \
14 & 47 & 52 & 47 & 49 & 48.75 & 5 \
15 & 52 & 57 & 58 & 52&54.75 & 6\
\end{array}$$

Accepted Answer

The answer of A machine is supposed to fill boxes...

Question 5

Use the given process data to construct a control chart for p
-Relate the concept of control charts to the concept of confidence intervals.

Accepted Answer

The answer of Use the given process data to construct...

Question 6

Use the given process data to construct a control chart for p
-A machine that is supposed to fill small bottles to contain 20 ml yields the following data from a test of 4 bottles every hour. 
$\begin{array}{l|llll|l|l}
S&&&A&&M&R\\hline
1 & 19.9 & 20.1 & 20.2 & 20.3&20 .125 & 0.4 \
2 & 20.4 & 20.0 & 20.3 & 20.3 & 20.25 & 0.4 \
3 & 20.0 & 20.7 & 20.4 & 20.3 & 20.35 & 0.7\
4 & 20.4 & 20.1 & 20.1 & 19.9&20 .125 & 0.5 \
5 & 19.9 & 19.8 & 19.6 & 19.5 & 19.7 & 0.4 \
6 & 19.4 & 19.4 & 19.6 & 19.7&19 .525 & 0.3\
7 & 19.8 & 19.4 & 19.6 & 19.7&19 .625&0 .4 \
8 & 19.9 & 19.8 & 20.0 & 20.0&19 .925 & 0.2 \
9 & 20.2 & 20.3 & 20.1 & 20.3&20 .225 & 0.2\
10 & 20.0 & 20.3 & 20.0 & 20.2&20 .125&0 .3 \
11 & 20.3 & 20.5 & 20.1 & 20.2&20 .275&0 .4 \
12 & 20.1 & 19.9 & 19.8 & 19.7&19 .875&0 .4\
13 & 19.5 & 19.8 & 19.7 & 19.6 & 19.65 & 0.3 \
14 & 19.4 & 19.8 & 19.8 & 19.4 & 19.4 & 0.4 \
15 & 19.5 & 19.6 & 19.6 & 19.9 & 19.65 & 0.4\
\end{array}$

Accepted Answer

The answer of Use the given process data to construct...

Question 7

Use the given process data to construct a control chart for p
-A machine that is supposed to fill small bottles to contain 20 ml yields the following data from a test of 4 bottles every hour. 
$\begin{array} { l|llll|l|  } S&&A&&&M&R\
\hline 
1&19.9&20.1&20.2&20.3&20.125&0.4\2&20.4&20.0&20.3&20.3&20.25&0.4\
3&20.0&20.7&20.4&20.3&20.35&0.7\4&20.4&20.1&20.1&19.9&20.125&0.5\
5&19.9&19.8&19.6&19.5&19.7&0.4\6&19.4&19.4&19.6&19.7&19.525&0.3\
7&19.8&19.4&19.6&19.7&19.625&0.4\8&19.9&19.8&20.0&20.0&19.925&0.2\
9&20.2&20.3&20.1&20.3&20.225&0.2\10&20.0&20.3&20.0&20.2&20.125&0.3\
11&20.3&20.5&20.1&20.2&20.275&0.4\12&20.1&19.9&19.8&19.7&19.875&0.4\
13&19.5&19.8&19.7&19.6&1965&0.3\14&19.4&19.8&19.8&19.4&19.4&0.4\
15&19.5&19.6&19.6&19.9&19.65&0.4
\end{array}$

Accepted Answer

The answer of Use the given process data to construct...

Question 8

Use the given process data to construct a control chart for p
-Define statistically stable (or "within statistical control"). Show examples of run charts which illustrate processes which are not statistically controlled. Discuss the pattern which indicates the process is not statistically controlled for each example.

Accepted Answer

The answer of Use the given process data to construct...

Question 9

A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below. $\begin{array}{l|llll|l|l}
S&&&A&&M&R\\hline
1 & 11.2 & 11.7 & 11.8 & 11 .7 & 11.6 & 0.6 \
2 & 11.8 & 11.3 & 11.6 & 11 .6 & 61.575 & 0.5 \
3 & 11.3 & 12.0 & 11.8 & 11.7 & 11.7 & 0.7 \
4 & 12.1 & 11.6 & 12.1 & 12 . 0& 11.95 & 0.5 \
5 & 11.8 & 11.8 & 11.9 & 11.9&11 .85 & 0.1\
6 & 12.0 & 11.9 & 11.8 & 11 .7& 11.85&0 .3 \
7 & 11.6 & 12.0 & 11.9 & 11.8 & 11.825&0 .4 \
8 & 11.5 & 12.1 & 11.9 & 12 .0& 11.875&0 .6 \
9 & 12.1 & 12.1 & 11.7 & 11.9&11 .95&0 .4\
10 & 11.7 & 12.0 & 11.6 & 11.9 & 11.8 & 0.4 \
11 & 12.1 & 12.4 & 11.9 & 12.2&12 .15 & 0.5 \
12 & 12.5 & 12.0 & 12.4 & 12.3 & 12.3 & 0.5\
13 & 12.5 & 12.0 & 12.1 & 12 .1& 12.175& 0.5 \
14 & 12.4 & 12.0 & 12.0 & 12.4 & 12.2 & 0.4 \
15 & 12.4 & 12.4 & 12.6 & 12 & 12.375 & 0.5\
\end{array}$

Accepted Answer

The answer of A machine is supposed to fill cans...

Question 10

Use the given process data to construct a control chart for p
-A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below. $\begin{array} { l|llll|l|  } S&&A&&&M&R\
\hline 
1&11.2&11.7&11.8&11.7&11.6&0.6\
2&11.8&11.3&11.6&11.6&11.575&0.5\
3&11.3&12.0&11.8&11.7&11.7&0.7\4&12.1&11.6&12.1&12.0&11.95&0.5\5&11.8&11.8&11.9&11.9&11.85&0.1\
6&12.0&11.9&11.8&11.7&11.85&0.3\
7&11.6&12.0&11.9&11.8&11.825&0.4\8&11.5&12.1&11.9&12.0&11.875&0.6\
9&12.1&12.1&11.7&11.9&11.95&0.4\
10&11.7&12.0&11.6&11.9&11.8&0.4\11&12.1&12.4&11.9&12.2&12.15&0.5\
12&12.5&12.0&12.4&12.3&12.3&0.5\13&12.5&12.0&12.1&12.1&12.175&0.5\
14&12.4&12.0&12.0&12.4&12.2&0.4\15&12.4&12.4&12.6&12.1&12.375&0.5
\end{array}$

Accepted Answer

The answer of Use the given process data to construct...

Question 11

Use the given process data to construct a control chart for p
-Draw a control chart that illustrates a process which is statistically stable and one which illustrates a process which is not statistically stable. Discuss the results.

Accepted Answer

The answer of Use the given process data to construct...

Question 12

Use the given process data to construct a control chart for p
-A machine that is supposed to produce ball bearings with a diameter of 7 mm yields the following data from a test of 5 ball bearings every 20 minutes. 
$\begin{array}{l|lllll|l|l}
S&&&A&&&M&R\\hline
1&6.3&6.8&6.9&6.8&6.9&6.74&0.5\
2 & 6.3 & 6.6 & 6.6 & 6.3 & 7.0&6 .56 & 0.7 \
3 & 6.8 & 6.7 & 7.0 & 6.5 & 7.0 & 6.8 & 0.5\
4 & 7.0 & 6.7 & 6.7 & 6.8 & 6.8 & 6.8 & 0.3 \
5 & 6.8 & 6.8 & 6.6 & 6.5 & 6.4&6 .62 & 0.4 \
6 & 6.8 & 6.7 & 6.6 & 6.3 & 6.9&6 .66 & 0.6\
7 & 7.3 & 7.3 & 7.4 & 7.4 & 7.0&7 .28 & 0.4 \
8 & 7.2 & 7.0 & 7.2 & 6.9 & 7.1&7 .08 & 0.3 \
9 & 7.3 & 7.6 & 7.1 & 7.4 & 7.6 & 7.4 & 0.5\
10 & 7.2 & 7.6 & 7.5 & 7.6 & 7.1 & 7.4 & 0.5 \
11 & 7.2 & 7.2 & 7.4 & 7.0 & 7.0&7 .16 & 0.4 \
12 & 7.5 & 7.4 & 7.4 & 7.6 & 7.1 & 7.4 & 0.5\
\end{array}$

Accepted Answer

The answer of Use the given process data to construct...

Question 13

Use the given process data to construct a control chart for p
-A machine is supposed to fill boxes to a weight of 50 lbs. Every 30 minutes a sample of four boxes is tested; the results are given below. $\begin{array}{l|llll|l|l}
S&&&A&&M&R\\hline
1 & 49 & 38 & 39 & 45 & 42.75 & 11 \
2 & 52 & 51 & 43 & 6 & 51.75 & 18 \
3 & 56 & 60 & 32 & 52 & 50 & 28\
4 & 44 & 59 & 46 & 49 & 49.5 & 15 \
5 & 51 & 61 & 48 & 45 & 51.25 & 16 \
6 & 45 & 50 & 46 & 48& 47.25 & 5 \
7 & 52 & 51 & 45 & 55& 50.75 & 10\
8 & 40 & 50 & 53 & 48 & 47.75 & 13 \
9 & 48 & 67 & 60 & 51 & 56.5 & 19 \
10 & 43 & 50 & 50 & 47 & 47.5 & 7 \
11 & 48 & 30 & 38 & 39 & 38.75 & 18\
12 & 50 & 46 & 48 & 53 & 49.25 & 7 \
13 & 50 & 58 & 56 & 64 & 57 & 14 \
14 & 47 & 52 & 47 & 49&48.75 & 5 \
15 & 52 & 57 & 58 & 52&54.75 & 6\
\end{array}$

Accepted Answer

The answer of Use the given process data to construct...

Question 14

Use the given process data to construct a control chart for p
-A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below. $\begin{array}{c|cccc|c|c}
\mathrm{S} & & \mathrm{A} &&& \mathrm{M} & \mathrm{R} \
\hline 1 & 11.2 & 11.7 & 11.8 & 11 .7 & 11.6 & 0.6 \
2 & 11.8 & 11.3 & 11.6 & 11 . 6& 1.575 & 0.5 \
3 & 11.3 & 12.0 & 11.8 & 11.7 & 11.7 & 0.7 \
4 & 12.1 & 11.6 & 12.1 & 12.0&11 .95 & 0.5 \
5 & 11.8 & 11.8 & 11.9 & 11.9&11 .85 & 0.1\
6 & 12.0 & 11.9 & 11.8 & 11.7&11 .85&0 .3 \
7 & 11.6 & 12.0 & 11.9 & 11.8&1 .825&0 .4 \
8 & 11.5 & 12.1 & 11.9 & 12.0&11 .875&0 .6\
9 & 12.1 & 12.1 & 11.7 & 11.9&11 .95&0 .4 \
10 & 11.7 & 12.0 & 11.6 & 11.9 & 11.8 & 0.4 \
11 & 12.1 & 12.4 & 11.9 & 12.2&12 .15&0 .5\
12 & 12.5 & 12.0 & 12.4 & 12 .3& 12.3 & 0.5 \
13 & 12.5 & 12.0 & 12.1 & 12.1 & 12.175 & 0.5 \
14 & 12.4 & 12.0 & 12.0 & 12 . 4& 12.2 & 0.4 \
15 & 12.4 & 12.4 & 12.6 & 12 .1 & 12.375 & 0.5\
\end{array}$

Accepted Answer

The answer of Use the given process data to construct...

Question 15

Use the given process data to construct a control chart for p
-Describe a control chart. Complete the table to identify the important parts of different types of control charts.
 $\begin{array}{r|c}
&&\text { Center line and } &\text {Upper } &\text { Lower } \
&\text { Points plotted } &\text {how to compute} &\text { control limit} &\text {control limit }\
\hline \text { Control char } \
\text { for } R \\
\text { Control char } \
\text { for } \bar{X} \\
\text { Control char } \
\text { for } p
\end{array}$

Accepted Answer

The answer of Use the given process data to construct...

Question 16

A machine that is supposed to produce ball bearings with a diameter of 7 mm yields the following data from a test of 5 ball bearings every 20 minutes. $\begin{array}{l|lllll|l|l}
S&&&A&&&M&R\\hline
1 & 6.3 & 6.8 & 6.9 & 6.8 & 6.9&6 .74 & 0.6 \
2 & 6.3 & 6.6 & 6.6 & 6.3 & 7.0&6 .56 & 0.7 \
3 & 6.8 & 6.7 & 7.0 & 6.5 & 7.0 & 6.8 & 0.5 \
4 & 7.0 & 6.7 & 6.7 & 6.8 & 6.8 & 6.8 & 0.3\
5 & 6.8 & 6.8 & 6.6 & 6.5 & 6.4&6 .62 & 0.4 \
6 & 6.8 & 6.7 & 6.6 & 6.3 & 6.9&6 .66 & 0.6 \
7 & 7.3 & 7.3 & 7.4 & 7.4 & 7.0&7 .28 & 0.4 \
8 & 7.2 & 7.0 & 7.2 & 6.9 & 7.1&7 .08&0 .3\
9 & 7.3 & 7.6 & 7.1 & 7.4 & 7.6 & 7.4 & 0.5 \
10 & 7.2 & 7.6 & 7.5 & 7.6 & 7.1 & 7.4 & 0.5 \
11 & 7.2 & 7.2 & 7.4 & 7.0 & 7.0&7 .16 & 0.4 \
12 & 7.5 & 7.4 & 7.4 & 7.6 & 7.1 & 7.4 & 0.5\
\end{array}$

Accepted Answer

The answer of A machine that is supposed to produce...

Question 17

Use the given process data to construct a control chart for p
-A machine is supposed to fill boxes to a weight of 50 lbs. Every 30 minutes a sample of four boxes is tested; the results are given below. 
$\begin{array} { l|llll|l|  } S&&A&&&M&R\
\hline 
1&49&38&39&45&42.75&11\2&52&51&43&61&51.75&18\
3&56&60&32&52&50&28\4&44&59&45&49&49.5&15\
5&51&61&48&45&51.25&16\6&45&50&46&48&47.25&5\
7&52&51&45&55&50.75&11\8&40&50&53&48&47.75&13\
9&48&67&60&51&56.5&19\10&43&50&50&47&47.5&7\11&48&30&38&39&38.75&18\12&50&46&48&53&49.25&7\
13&50&58&56&64&57&14\14&47&52&47&49&48.75&5\15&52&57&58&52&54.75&6
\end{array}$

Accepted Answer

The answer of Use the given process data to construct...

Question 18

Use the given process data to construct a control chart for p
-Describe the three criteria used to determine if a control chart indicates a process which is not statistically stable.

Accepted Answer

The answer of Use the given process data to construct...

Question 19

Use the given process data to construct a control chart for p
-Describe what process data are. Why are process data important to businesses? What is a common goal of businesses using quality control?

Accepted Answer

The answer of Use the given process data to construct...

Question 20

Use the given process data to construct a control chart for p
-A common goal of quality control is to reduce variation in a product or service. List and describe the two types of variability. Give an example of each.

Accepted Answer

The answer of Use the given process data to construct...

Quiz 14: Statistical Process Control

Use the given process data to construct a control chart for p -Describe a run chart and give an example. Refer to the values on each of the axes as you describe the run chart.

Use the given process data to construct a control chart for p -Relate the concept of control charts to the concept of confidence intervals.

Use the given process data to construct a control chart for p -Draw a control chart that illustrates a process which is statistically stable and one which illustrates a process which is not statistically stable. Discuss the results.

Use the given process data to construct a control chart for p -Describe the three criteria used to determine if a control chart indicates a process which is not statistically stable.

Use the given process data to construct a control chart for p -Describe what process data are. Why are process data important to businesses? What is a common goal of businesses using quality control?

Use the given process data to construct a control chart for p -A common goal of quality control is to reduce variation in a product or service. List and describe the two types of variability. Give an example of each.