The Standard Deviation of the Overall Process Is Known to Be 0.17 Ounces
Question 1
The Safi Pottery Company in Morocco has been making a specific style of tagine that has been very popular in Europe for over 1,000 years. The phosphorous used in the tagines ranges from 1.0 to 1.8 grams. There is a problem if the phosphorous weighs less than 1.0 grams [too brittle] or more than 1.8 grams [hard to mold] so maintaining quality control is critical. The company has one production line that measures the weight of the phosphorous that goes into each tagine. Recently some of the tagines have been not met specifications and distributors have been complaining and threatening to find new producers.
Sample
Obs / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 121 / 1.8 / 1.0 / 1.8 / 1.6 / 1.7 / 1.0 / 1.3 / 1.3 / 1.8 / 1.8 / 1.2 / 1.6
2 / 1.1 / 1.6 / 1.2 / 1.5 / 1.5 / 1.3 / 1.1 / 1.6 / 1.2 / 1.6 / 1.8 / 1.2
3 / 1.6 / 1.3 / 1.7 / 1.3 / 1.3 / 1.6 / 1.6 / 1.5 / 1.3 / 1.2 / 1.7 / 1.3
4 / 1.4 / 1.5 / 1.8 / 1.1 / 1.6 / 1.2 / 1.4 / 1.3 / 1.7 / 1.7 / 1.8 / 1.6
5 / 1.1 / 1.1 / 1.2 / 1.8 / 1.8 / 1.1 / 1.8 / 1.5 / 1.8 / 1.6 / 1.1 / 1.3
6 / 1.0 / 1.4 / 1.8 / 1.3 / 1.8 / 1.0 / 1.6 / 1.4 / 1.8 / 1.7 / 1.1 / 1.5
7 / 1.2 / 1.0 / 1.8 / 1.3 / 1.5 / 1.7 / 1.5 / 1.2 / 1.4 / 1.1 / 1.7 / 1.0
8 / 1.7 / 1.7 / 1.2 / 1.7 / 1.4 / 1.0 / 1.0 / 1.4 / 1.5 / 1.3 / 1.4 / 1.0
9 / 1.7 / 1.0 / 1.0 / 1.1 / 1.5 / 1.6 / 1.6 / 1.4 / 1.3 / 1.1 / 1.0 / 1.3
10 / 1.8 / 1.0 / 1.6 / 1.2 / 1.1 / 1.1 / 1.8 / 1.7 / 1.4 / 1.1 / 1.3 / 1.7
11 / 1.2 / 1.3 / 1.1 / 1.0 / 1.4 / 1.4 / 1.5 / 1.6 / 1.6 / 1.2 / 1.2 / 1.0
12 / 1.4 / 1.7 / 1.8 / 1.7 / 1.2 / 1.3 / 1.6 / 1.5 / 1.8 / 1.1 / 1.2 / 1.7
13 / 1.4 / 1.2 / 1.4 / 1.7 / 1.0 / 1.8 / 1.6 / 1.5 / 1.7 / 1.5 / 1.7 / 1.5
14 / 1.2 / 1.5 / 1.1 / 1.3 / 1.0 / 1.2 / 1.5 / 1.7 / 1.5 / 1.0 / 1.0 / 1.6
15 / 1.5 / 1.7 / 1.3 / 1.8 / 1.0 / 1.4 / 1.6 / 1.3 / 1.1 / 1.0 / 1.1 / 1.0
16 / 1.2 / 1.8 / 1.5 / 1.6 / 1.0 / 1.5 / 1.2 / 1.1 / 1.4 / 1.8 / 1.0 / 1.2
17 / 1.2 / 1.6 / 1.6 / 1.0 / 1.6 / 1.7 / 1.8 / 1.5 / 1.7 / 1.3 / 1.4 / 1.4
18 / 1.5 / 1.6 / 1.2 / 1.8 / 1.3 / 1.6 / 1.0 / 1.7 / 1.6 / 1.4 / 1.5 / 1.3
19 / 1.3 / 1.2 / 1.5 / 1.6 / 1.6 / 1.3 / 1.2 / 1.8 / 1.3 / 1.1 / 1.7 / 1.7
20 / 1.5 / 1.5 / 1.0 / 1.7 / 1.1 / 1.3 / 1.0 / 1.6 / 1.5 / 1.1 / 1.2 / 1.7
21 / 1.1 / 1.2 / 1.1 / 1.4 / 1.7 / 1.7 / 1.7 / 1.5 / 1.1 / 1.0 / 1.7 / 1.0
22 / 1.0 / 1.6 / 1.5 / 1.7 / 1.4 / 1.8 / 1.1 / 1.8 / 1.0 / 1.8 / 1.6 / 1.6
23 / 1.4 / 1.1 / 1.3 / 1.6 / 1.8 / 1.1 / 1.1 / 1.4 / 1.6 / 1.8 / 1.2 / 1.8
24 / 1.8 / 1.0 / 1.3 / 1.5 / 1.2 / 1.6 / 1.5 / 1.7 / 1.1 / 1.0 / 1.5 / 1.2
25 / 1.3 / 1.1 / 1.0 / 1.6 / 1.0 / 1.6 / 1.2 / 1.2 / 1.1 / 1.2 / 1.4 / 1.4
The standard deviation of the overall process is known to be 0.17 ounces.
What is the upper control limit of 3 standard deviations?
Answer:
Question 2
The Safi Pottery Company in Morocco has been making a specific style of tagine that has been very popular in Europe for over 1,000 years. The phosphorous used in the tagines ranges from 1.0 to 1.8 grams. There is a problem if the phosphorous weighs less than 1.0 grams [too brittle] or more than 1.8 grams [hard to mold] so maintaining quality control is critical. The company has one production line that measures the weight of the phosphorous that goes into each tagine. Recently some of the tagines have been not met specifications and distributors have been complaining and threatening to find new producers.
Sample
Obs / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 121 / 1.8 / 1.0 / 1.8 / 1.6 / 1.7 / 1.0 / 1.3 / 1.3 / 1.8 / 1.8 / 1.2 / 1.6
2 / 1.1 / 1.6 / 1.2 / 1.5 / 1.5 / 1.3 / 1.1 / 1.6 / 1.2 / 1.6 / 1.8 / 1.2
3 / 1.6 / 1.3 / 1.7 / 1.3 / 1.3 / 1.6 / 1.6 / 1.5 / 1.3 / 1.2 / 1.7 / 1.3
4 / 1.4 / 1.5 / 1.8 / 1.1 / 1.6 / 1.2 / 1.4 / 1.3 / 1.7 / 1.7 / 1.8 / 1.6
5 / 1.1 / 1.1 / 1.2 / 1.8 / 1.8 / 1.1 / 1.8 / 1.5 / 1.8 / 1.6 / 1.1 / 1.3
6 / 1.0 / 1.4 / 1.8 / 1.3 / 1.8 / 1.0 / 1.6 / 1.4 / 1.8 / 1.7 / 1.1 / 1.5
7 / 1.2 / 1.0 / 1.8 / 1.3 / 1.5 / 1.7 / 1.5 / 1.2 / 1.4 / 1.1 / 1.7 / 1.0
8 / 1.7 / 1.7 / 1.2 / 1.7 / 1.4 / 1.0 / 1.0 / 1.4 / 1.5 / 1.3 / 1.4 / 1.0
9 / 1.7 / 1.0 / 1.0 / 1.1 / 1.5 / 1.6 / 1.6 / 1.4 / 1.3 / 1.1 / 1.0 / 1.3
10 / 1.8 / 1.0 / 1.6 / 1.2 / 1.1 / 1.1 / 1.8 / 1.7 / 1.4 / 1.1 / 1.3 / 1.7
11 / 1.2 / 1.3 / 1.1 / 1.0 / 1.4 / 1.4 / 1.5 / 1.6 / 1.6 / 1.2 / 1.2 / 1.0
12 / 1.4 / 1.7 / 1.8 / 1.7 / 1.2 / 1.3 / 1.6 / 1.5 / 1.8 / 1.1 / 1.2 / 1.7
13 / 1.4 / 1.2 / 1.4 / 1.7 / 1.0 / 1.8 / 1.6 / 1.5 / 1.7 / 1.5 / 1.7 / 1.5
14 / 1.2 / 1.5 / 1.1 / 1.3 / 1.0 / 1.2 / 1.5 / 1.7 / 1.5 / 1.0 / 1.0 / 1.6
15 / 1.5 / 1.7 / 1.3 / 1.8 / 1.0 / 1.4 / 1.6 / 1.3 / 1.1 / 1.0 / 1.1 / 1.0
16 / 1.2 / 1.8 / 1.5 / 1.6 / 1.0 / 1.5 / 1.2 / 1.1 / 1.4 / 1.8 / 1.0 / 1.2
17 / 1.2 / 1.6 / 1.6 / 1.0 / 1.6 / 1.7 / 1.8 / 1.5 / 1.7 / 1.3 / 1.4 / 1.4
18 / 1.5 / 1.6 / 1.2 / 1.8 / 1.3 / 1.6 / 1.0 / 1.7 / 1.6 / 1.4 / 1.5 / 1.3
19 / 1.3 / 1.2 / 1.5 / 1.6 / 1.6 / 1.3 / 1.2 / 1.8 / 1.3 / 1.1 / 1.7 / 1.7
20 / 1.5 / 1.5 / 1.0 / 1.7 / 1.1 / 1.3 / 1.0 / 1.6 / 1.5 / 1.1 / 1.2 / 1.7
21 / 1.1 / 1.2 / 1.1 / 1.4 / 1.7 / 1.7 / 1.7 / 1.5 / 1.1 / 1.0 / 1.7 / 1.0
22 / 1.0 / 1.6 / 1.5 / 1.7 / 1.4 / 1.8 / 1.1 / 1.8 / 1.0 / 1.8 / 1.6 / 1.6
23 / 1.4 / 1.1 / 1.3 / 1.6 / 1.8 / 1.1 / 1.1 / 1.4 / 1.6 / 1.8 / 1.2 / 1.8
24 / 1.8 / 1.0 / 1.3 / 1.5 / 1.2 / 1.6 / 1.5 / 1.7 / 1.1 / 1.0 / 1.5 / 1.2
25 / 1.3 / 1.1 / 1.0 / 1.6 / 1.0 / 1.6 / 1.2 / 1.2 / 1.1 / 1.2 / 1.4 / 1.4
The standard deviation of the overall process is known to be 0.17 ounces.
What is the lower control limit of 3 standard deviations?
Answer:
Question 3
The Safi Pottery Company in Morocco has been making a specific style of tagine that has been very popular in Europe for over 1,000 years. The phosphorous used in the tagines ranges from 1.0 to 1.8 grams. There is a problem if the phosphorous weighs less than 1.0 grams [too brittle] or more than 1.8 grams [hard to mold] so maintaining quality control is critical. The company has one production line that measures the weight of the phosphorous that goes into each tagine. Recently some of the tagines have been not met specifications and distributors have been complaining and threatening to find new producers.
Sample
Obs / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 121 / 1.8 / 1.0 / 1.8 / 1.6 / 1.7 / 1.0 / 1.3 / 1.3 / 1.8 / 1.8 / 1.2 / 1.6
2 / 1.1 / 1.6 / 1.2 / 1.5 / 1.5 / 1.3 / 1.1 / 1.6 / 1.2 / 1.6 / 1.8 / 1.2
3 / 1.6 / 1.3 / 1.7 / 1.3 / 1.3 / 1.6 / 1.6 / 1.5 / 1.3 / 1.2 / 1.7 / 1.3
4 / 1.4 / 1.5 / 1.8 / 1.1 / 1.6 / 1.2 / 1.4 / 1.3 / 1.7 / 1.7 / 1.8 / 1.6
5 / 1.1 / 1.1 / 1.2 / 1.8 / 1.8 / 1.1 / 1.8 / 1.5 / 1.8 / 1.6 / 1.1 / 1.3
6 / 1.0 / 1.4 / 1.8 / 1.3 / 1.8 / 1.0 / 1.6 / 1.4 / 1.8 / 1.7 / 1.1 / 1.5
7 / 1.2 / 1.0 / 1.8 / 1.3 / 1.5 / 1.7 / 1.5 / 1.2 / 1.4 / 1.1 / 1.7 / 1.0
8 / 1.7 / 1.7 / 1.2 / 1.7 / 1.4 / 1.0 / 1.0 / 1.4 / 1.5 / 1.3 / 1.4 / 1.0
9 / 1.7 / 1.0 / 1.0 / 1.1 / 1.5 / 1.6 / 1.6 / 1.4 / 1.3 / 1.1 / 1.0 / 1.3
10 / 1.8 / 1.0 / 1.6 / 1.2 / 1.1 / 1.1 / 1.8 / 1.7 / 1.4 / 1.1 / 1.3 / 1.7
11 / 1.2 / 1.3 / 1.1 / 1.0 / 1.4 / 1.4 / 1.5 / 1.6 / 1.6 / 1.2 / 1.2 / 1.0
12 / 1.4 / 1.7 / 1.8 / 1.7 / 1.2 / 1.3 / 1.6 / 1.5 / 1.8 / 1.1 / 1.2 / 1.7
13 / 1.4 / 1.2 / 1.4 / 1.7 / 1.0 / 1.8 / 1.6 / 1.5 / 1.7 / 1.5 / 1.7 / 1.5
14 / 1.2 / 1.5 / 1.1 / 1.3 / 1.0 / 1.2 / 1.5 / 1.7 / 1.5 / 1.0 / 1.0 / 1.6
15 / 1.5 / 1.7 / 1.3 / 1.8 / 1.0 / 1.4 / 1.6 / 1.3 / 1.1 / 1.0 / 1.1 / 1.0
16 / 1.2 / 1.8 / 1.5 / 1.6 / 1.0 / 1.5 / 1.2 / 1.1 / 1.4 / 1.8 / 1.0 / 1.2
17 / 1.2 / 1.6 / 1.6 / 1.0 / 1.6 / 1.7 / 1.8 / 1.5 / 1.7 / 1.3 / 1.4 / 1.4
18 / 1.5 / 1.6 / 1.2 / 1.8 / 1.3 / 1.6 / 1.0 / 1.7 / 1.6 / 1.4 / 1.5 / 1.3
19 / 1.3 / 1.2 / 1.5 / 1.6 / 1.6 / 1.3 / 1.2 / 1.8 / 1.3 / 1.1 / 1.7 / 1.7
20 / 1.5 / 1.5 / 1.0 / 1.7 / 1.1 / 1.3 / 1.0 / 1.6 / 1.5 / 1.1 / 1.2 / 1.7
21 / 1.1 / 1.2 / 1.1 / 1.4 / 1.7 / 1.7 / 1.7 / 1.5 / 1.1 / 1.0 / 1.7 / 1.0
22 / 1.0 / 1.6 / 1.5 / 1.7 / 1.4 / 1.8 / 1.1 / 1.8 / 1.0 / 1.8 / 1.6 / 1.6
23 / 1.4 / 1.1 / 1.3 / 1.6 / 1.8 / 1.1 / 1.1 / 1.4 / 1.6 / 1.8 / 1.2 / 1.8
24 / 1.8 / 1.0 / 1.3 / 1.5 / 1.2 / 1.6 / 1.5 / 1.7 / 1.1 / 1.0 / 1.5 / 1.2
25 / 1.3 / 1.1 / 1.0 / 1.6 / 1.0 / 1.6 / 1.2 / 1.2 / 1.1 / 1.2 / 1.4 / 1.4
The standard deviation of the overall process is known to be 0.17 ounces.
Using the following range chart develop a 3-sigma upper control limit for the operation assuming the standard deviation is the same as the range.
Sample Size / A2 Factor R Chart / D3 Factor R Chart / D4 Factor R Chart2 / 1.83 / 0.00 / 3.27
3 / 1.02 / 0.00 / 2.57
4 / 0.73 / 0.00 / 2.28
5 / 0.58 / 0.00 / 2.11
6 / 0.48 / 0.00 / 2.00
7 / 0.42 / 0.08 / 1.92
8 / 0.37 / 0.14 / 1.86
9 / 0.34 / 0.18 / 1.82
10 / 0.31 / 0.22 / 1.78
11 / 0.29 / 0.26 / 1.74
12 / 0.27 / 0.28 / 1.72
13 / 0.25 / 0.31 / 1.69
14 / 0.24 / 0.33 / 1.67
15 / 0.22 / 0.35 / 1.65
16 / 0.21 / 0.36 / 1.64
17 / 0.20 / 0.38 / 1.62
18 / 0.19 / 0.39 / 1.61
19 / 0.19 / 0.40 / 1.60
20 / 0.18 / 0.41 / 1.59
21 / 0.17 / 0.43 / 1.58
22 / 0.17 / 0.43 / 1.57
23 / 0.16 / 0.44 / 1.56
24 / 0.16 / 0.45 / 1.55
25 / 0.15 / 0.46 / 1.54
Answer:
Question 4
The Safi Pottery Company in Morocco has been making a specific style of tagine that has been very popular in Europe for over 1,000 years. The phosphorous used in the tagines ranges from 1.0 to 1.8 grams. There is a problem if the phosphorous weighs less than 1.0 grams [too brittle] or more than 1.8 grams [hard to mold] so maintaining quality control is critical. The company has one production line that measures the weight of the phosphorous that goes into each tagine. Recently some of the tagines have been not met specifications and distributors have been complaining and threatening to find new producers.
Sample
Obs / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 121 / 1.8 / 1.0 / 1.8 / 1.6 / 1.7 / 1.0 / 1.3 / 1.3 / 1.8 / 1.8 / 1.2 / 1.6
2 / 1.1 / 1.6 / 1.2 / 1.5 / 1.5 / 1.3 / 1.1 / 1.6 / 1.2 / 1.6 / 1.8 / 1.2
3 / 1.6 / 1.3 / 1.7 / 1.3 / 1.3 / 1.6 / 1.6 / 1.5 / 1.3 / 1.2 / 1.7 / 1.3
4 / 1.4 / 1.5 / 1.8 / 1.1 / 1.6 / 1.2 / 1.4 / 1.3 / 1.7 / 1.7 / 1.8 / 1.6
5 / 1.1 / 1.1 / 1.2 / 1.8 / 1.8 / 1.1 / 1.8 / 1.5 / 1.8 / 1.6 / 1.1 / 1.3
6 / 1.0 / 1.4 / 1.8 / 1.3 / 1.8 / 1.0 / 1.6 / 1.4 / 1.8 / 1.7 / 1.1 / 1.5
7 / 1.2 / 1.0 / 1.8 / 1.3 / 1.5 / 1.7 / 1.5 / 1.2 / 1.4 / 1.1 / 1.7 / 1.0
8 / 1.7 / 1.7 / 1.2 / 1.7 / 1.4 / 1.0 / 1.0 / 1.4 / 1.5 / 1.3 / 1.4 / 1.0
9 / 1.7 / 1.0 / 1.0 / 1.1 / 1.5 / 1.6 / 1.6 / 1.4 / 1.3 / 1.1 / 1.0 / 1.3
10 / 1.8 / 1.0 / 1.6 / 1.2 / 1.1 / 1.1 / 1.8 / 1.7 / 1.4 / 1.1 / 1.3 / 1.7
11 / 1.2 / 1.3 / 1.1 / 1.0 / 1.4 / 1.4 / 1.5 / 1.6 / 1.6 / 1.2 / 1.2 / 1.0
12 / 1.4 / 1.7 / 1.8 / 1.7 / 1.2 / 1.3 / 1.6 / 1.5 / 1.8 / 1.1 / 1.2 / 1.7
13 / 1.4 / 1.2 / 1.4 / 1.7 / 1.0 / 1.8 / 1.6 / 1.5 / 1.7 / 1.5 / 1.7 / 1.5
14 / 1.2 / 1.5 / 1.1 / 1.3 / 1.0 / 1.2 / 1.5 / 1.7 / 1.5 / 1.0 / 1.0 / 1.6
15 / 1.5 / 1.7 / 1.3 / 1.8 / 1.0 / 1.4 / 1.6 / 1.3 / 1.1 / 1.0 / 1.1 / 1.0
16 / 1.2 / 1.8 / 1.5 / 1.6 / 1.0 / 1.5 / 1.2 / 1.1 / 1.4 / 1.8 / 1.0 / 1.2
17 / 1.2 / 1.6 / 1.6 / 1.0 / 1.6 / 1.7 / 1.8 / 1.5 / 1.7 / 1.3 / 1.4 / 1.4
18 / 1.5 / 1.6 / 1.2 / 1.8 / 1.3 / 1.6 / 1.0 / 1.7 / 1.6 / 1.4 / 1.5 / 1.3
19 / 1.3 / 1.2 / 1.5 / 1.6 / 1.6 / 1.3 / 1.2 / 1.8 / 1.3 / 1.1 / 1.7 / 1.7
20 / 1.5 / 1.5 / 1.0 / 1.7 / 1.1 / 1.3 / 1.0 / 1.6 / 1.5 / 1.1 / 1.2 / 1.7
21 / 1.1 / 1.2 / 1.1 / 1.4 / 1.7 / 1.7 / 1.7 / 1.5 / 1.1 / 1.0 / 1.7 / 1.0
22 / 1.0 / 1.6 / 1.5 / 1.7 / 1.4 / 1.8 / 1.1 / 1.8 / 1.0 / 1.8 / 1.6 / 1.6
23 / 1.4 / 1.1 / 1.3 / 1.6 / 1.8 / 1.1 / 1.1 / 1.4 / 1.6 / 1.8 / 1.2 / 1.8
24 / 1.8 / 1.0 / 1.3 / 1.5 / 1.2 / 1.6 / 1.5 / 1.7 / 1.1 / 1.0 / 1.5 / 1.2
25 / 1.3 / 1.1 / 1.0 / 1.6 / 1.0 / 1.6 / 1.2 / 1.2 / 1.1 / 1.2 / 1.4 / 1.4
The standard deviation of the overall process is known to be 0.17 ounces.
Using the following range chart develop a 3-sigma lower control limit for the operation assuming the standard deviation is the same as the range.
Sample Size / A2 Factor R Chart / D3 Factor R Chart / D4 Factor R Chart2 / 1.83 / 0.00 / 3.27
3 / 1.02 / 0.00 / 2.57
4 / 0.73 / 0.00 / 2.28
5 / 0.58 / 0.00 / 2.11
6 / 0.48 / 0.00 / 2.00
7 / 0.42 / 0.08 / 1.92
8 / 0.37 / 0.14 / 1.86
9 / 0.34 / 0.18 / 1.82
10 / 0.31 / 0.22 / 1.78
11 / 0.29 / 0.26 / 1.74
12 / 0.27 / 0.28 / 1.72
13 / 0.25 / 0.31 / 1.69
14 / 0.24 / 0.33 / 1.67
15 / 0.22 / 0.35 / 1.65
16 / 0.21 / 0.36 / 1.64
17 / 0.20 / 0.38 / 1.62
18 / 0.19 / 0.39 / 1.61
19 / 0.19 / 0.40 / 1.60
20 / 0.18 / 0.41 / 1.59
21 / 0.17 / 0.43 / 1.58
22 / 0.17 / 0.43 / 1.57
23 / 0.16 / 0.44 / 1.56
24 / 0.16 / 0.45 / 1.55
25 / 0.15 / 0.46 / 1.54
Answer:
Question 5
The Safi Pottery Company in Morocco has been making a specific style of tagine that has been very popular in Europe for over 1,000 years. The phosphorous used in the tagines ranges from 1.0 to 1.8 grams. There is a problem if the phosphorous weighs less than 1.0 grams [too brittle] or more than 1.8 grams [hard to mold] so maintaining quality control is critical. The company has one production line that measures the weight of the phosphorous that goes into each tagine. Recently some of the tagines have been not met specifications and distributors have been complaining and threatening to find new producers.
Sample
Obs / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 121 / 1.8 / 1.0 / 1.8 / 1.6 / 1.7 / 1.0 / 1.3 / 1.3 / 1.8 / 1.8 / 1.2 / 1.6
2 / 1.1 / 1.6 / 1.2 / 1.5 / 1.5 / 1.3 / 1.1 / 1.6 / 1.2 / 1.6 / 1.8 / 1.2
3 / 1.6 / 1.3 / 1.7 / 1.3 / 1.3 / 1.6 / 1.6 / 1.5 / 1.3 / 1.2 / 1.7 / 1.3
4 / 1.4 / 1.5 / 1.8 / 1.1 / 1.6 / 1.2 / 1.4 / 1.3 / 1.7 / 1.7 / 1.8 / 1.6
5 / 1.1 / 1.1 / 1.2 / 1.8 / 1.8 / 1.1 / 1.8 / 1.5 / 1.8 / 1.6 / 1.1 / 1.3
6 / 1.0 / 1.4 / 1.8 / 1.3 / 1.8 / 1.0 / 1.6 / 1.4 / 1.8 / 1.7 / 1.1 / 1.5
7 / 1.2 / 1.0 / 1.8 / 1.3 / 1.5 / 1.7 / 1.5 / 1.2 / 1.4 / 1.1 / 1.7 / 1.0
8 / 1.7 / 1.7 / 1.2 / 1.7 / 1.4 / 1.0 / 1.0 / 1.4 / 1.5 / 1.3 / 1.4 / 1.0
9 / 1.7 / 1.0 / 1.0 / 1.1 / 1.5 / 1.6 / 1.6 / 1.4 / 1.3 / 1.1 / 1.0 / 1.3
10 / 1.8 / 1.0 / 1.6 / 1.2 / 1.1 / 1.1 / 1.8 / 1.7 / 1.4 / 1.1 / 1.3 / 1.7
11 / 1.2 / 1.3 / 1.1 / 1.0 / 1.4 / 1.4 / 1.5 / 1.6 / 1.6 / 1.2 / 1.2 / 1.0
12 / 1.4 / 1.7 / 1.8 / 1.7 / 1.2 / 1.3 / 1.6 / 1.5 / 1.8 / 1.1 / 1.2 / 1.7
13 / 1.4 / 1.2 / 1.4 / 1.7 / 1.0 / 1.8 / 1.6 / 1.5 / 1.7 / 1.5 / 1.7 / 1.5
14 / 1.2 / 1.5 / 1.1 / 1.3 / 1.0 / 1.2 / 1.5 / 1.7 / 1.5 / 1.0 / 1.0 / 1.6
15 / 1.5 / 1.7 / 1.3 / 1.8 / 1.0 / 1.4 / 1.6 / 1.3 / 1.1 / 1.0 / 1.1 / 1.0
16 / 1.2 / 1.8 / 1.5 / 1.6 / 1.0 / 1.5 / 1.2 / 1.1 / 1.4 / 1.8 / 1.0 / 1.2
17 / 1.2 / 1.6 / 1.6 / 1.0 / 1.6 / 1.7 / 1.8 / 1.5 / 1.7 / 1.3 / 1.4 / 1.4
18 / 1.5 / 1.6 / 1.2 / 1.8 / 1.3 / 1.6 / 1.0 / 1.7 / 1.6 / 1.4 / 1.5 / 1.3
19 / 1.3 / 1.2 / 1.5 / 1.6 / 1.6 / 1.3 / 1.2 / 1.8 / 1.3 / 1.1 / 1.7 / 1.7
20 / 1.5 / 1.5 / 1.0 / 1.7 / 1.1 / 1.3 / 1.0 / 1.6 / 1.5 / 1.1 / 1.2 / 1.7
21 / 1.1 / 1.2 / 1.1 / 1.4 / 1.7 / 1.7 / 1.7 / 1.5 / 1.1 / 1.0 / 1.7 / 1.0
22 / 1.0 / 1.6 / 1.5 / 1.7 / 1.4 / 1.8 / 1.1 / 1.8 / 1.0 / 1.8 / 1.6 / 1.6
23 / 1.4 / 1.1 / 1.3 / 1.6 / 1.8 / 1.1 / 1.1 / 1.4 / 1.6 / 1.8 / 1.2 / 1.8
24 / 1.8 / 1.0 / 1.3 / 1.5 / 1.2 / 1.6 / 1.5 / 1.7 / 1.1 / 1.0 / 1.5 / 1.2
25 / 1.3 / 1.1 / 1.0 / 1.6 / 1.0 / 1.6 / 1.2 / 1.2 / 1.1 / 1.2 / 1.4 / 1.4
A sample was taken the range was found to be 0.21. Using the following range chart what is the upper control limit for the sample range?
Sample Size / A2 Factor R Chart / D3 Factor R Chart / D4 Factor R Chart2 / 1.83 / 0.00 / 3.27
3 / 1.02 / 0.00 / 2.57
4 / 0.73 / 0.00 / 2.28
5 / 0.58 / 0.00 / 2.11
6 / 0.48 / 0.00 / 2.00
7 / 0.42 / 0.08 / 1.92
8 / 0.37 / 0.14 / 1.86
9 / 0.34 / 0.18 / 1.82
10 / 0.31 / 0.22 / 1.78
11 / 0.29 / 0.26 / 1.74
12 / 0.27 / 0.28 / 1.72
13 / 0.25 / 0.31 / 1.69
14 / 0.24 / 0.33 / 1.67
15 / 0.22 / 0.35 / 1.65
16 / 0.21 / 0.36 / 1.64
17 / 0.20 / 0.38 / 1.62
18 / 0.19 / 0.39 / 1.61
19 / 0.19 / 0.40 / 1.60
20 / 0.18 / 0.41 / 1.59
21 / 0.17 / 0.43 / 1.58
22 / 0.17 / 0.43 / 1.57
23 / 0.16 / 0.44 / 1.56
24 / 0.16 / 0.45 / 1.55
25 / 0.15 / 0.46 / 1.54
Answer:
Question 6
The Safi Pottery Company in Morocco has been making a specific style of tagine that has been very popular in Europe for over 1,000 years. The phosphorous used in the tagines ranges from 1.0 to 1.8 grams. There is a problem if the phosphorous weighs less than 1.0 grams [too brittle] or more than 1.8 grams [hard to mold] so maintaining quality control is critical. The company has one production line that measures the weight of the phosphorous that goes into each tagine. Recently some of the tagines have been not met specifications and distributors have been complaining and threatening to find new producers.
Sample
Obs / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 121 / 1.8 / 1.0 / 1.8 / 1.6 / 1.7 / 1.0 / 1.3 / 1.3 / 1.8 / 1.8 / 1.2 / 1.6
2 / 1.1 / 1.6 / 1.2 / 1.5 / 1.5 / 1.3 / 1.1 / 1.6 / 1.2 / 1.6 / 1.8 / 1.2
3 / 1.6 / 1.3 / 1.7 / 1.3 / 1.3 / 1.6 / 1.6 / 1.5 / 1.3 / 1.2 / 1.7 / 1.3
4 / 1.4 / 1.5 / 1.8 / 1.1 / 1.6 / 1.2 / 1.4 / 1.3 / 1.7 / 1.7 / 1.8 / 1.6
5 / 1.1 / 1.1 / 1.2 / 1.8 / 1.8 / 1.1 / 1.8 / 1.5 / 1.8 / 1.6 / 1.1 / 1.3
6 / 1.0 / 1.4 / 1.8 / 1.3 / 1.8 / 1.0 / 1.6 / 1.4 / 1.8 / 1.7 / 1.1 / 1.5
7 / 1.2 / 1.0 / 1.8 / 1.3 / 1.5 / 1.7 / 1.5 / 1.2 / 1.4 / 1.1 / 1.7 / 1.0
8 / 1.7 / 1.7 / 1.2 / 1.7 / 1.4 / 1.0 / 1.0 / 1.4 / 1.5 / 1.3 / 1.4 / 1.0
9 / 1.7 / 1.0 / 1.0 / 1.1 / 1.5 / 1.6 / 1.6 / 1.4 / 1.3 / 1.1 / 1.0 / 1.3
10 / 1.8 / 1.0 / 1.6 / 1.2 / 1.1 / 1.1 / 1.8 / 1.7 / 1.4 / 1.1 / 1.3 / 1.7
11 / 1.2 / 1.3 / 1.1 / 1.0 / 1.4 / 1.4 / 1.5 / 1.6 / 1.6 / 1.2 / 1.2 / 1.0
12 / 1.4 / 1.7 / 1.8 / 1.7 / 1.2 / 1.3 / 1.6 / 1.5 / 1.8 / 1.1 / 1.2 / 1.7
13 / 1.4 / 1.2 / 1.4 / 1.7 / 1.0 / 1.8 / 1.6 / 1.5 / 1.7 / 1.5 / 1.7 / 1.5
14 / 1.2 / 1.5 / 1.1 / 1.3 / 1.0 / 1.2 / 1.5 / 1.7 / 1.5 / 1.0 / 1.0 / 1.6
15 / 1.5 / 1.7 / 1.3 / 1.8 / 1.0 / 1.4 / 1.6 / 1.3 / 1.1 / 1.0 / 1.1 / 1.0
16 / 1.2 / 1.8 / 1.5 / 1.6 / 1.0 / 1.5 / 1.2 / 1.1 / 1.4 / 1.8 / 1.0 / 1.2
17 / 1.2 / 1.6 / 1.6 / 1.0 / 1.6 / 1.7 / 1.8 / 1.5 / 1.7 / 1.3 / 1.4 / 1.4
18 / 1.5 / 1.6 / 1.2 / 1.8 / 1.3 / 1.6 / 1.0 / 1.7 / 1.6 / 1.4 / 1.5 / 1.3
19 / 1.3 / 1.2 / 1.5 / 1.6 / 1.6 / 1.3 / 1.2 / 1.8 / 1.3 / 1.1 / 1.7 / 1.7
20 / 1.5 / 1.5 / 1.0 / 1.7 / 1.1 / 1.3 / 1.0 / 1.6 / 1.5 / 1.1 / 1.2 / 1.7
21 / 1.1 / 1.2 / 1.1 / 1.4 / 1.7 / 1.7 / 1.7 / 1.5 / 1.1 / 1.0 / 1.7 / 1.0
22 / 1.0 / 1.6 / 1.5 / 1.7 / 1.4 / 1.8 / 1.1 / 1.8 / 1.0 / 1.8 / 1.6 / 1.6
23 / 1.4 / 1.1 / 1.3 / 1.6 / 1.8 / 1.1 / 1.1 / 1.4 / 1.6 / 1.8 / 1.2 / 1.8
24 / 1.8 / 1.0 / 1.3 / 1.5 / 1.2 / 1.6 / 1.5 / 1.7 / 1.1 / 1.0 / 1.5 / 1.2
25 / 1.3 / 1.1 / 1.0 / 1.6 / 1.0 / 1.6 / 1.2 / 1.2 / 1.1 / 1.2 / 1.4 / 1.4
A sample was taken the range was found to be 0.21. Using the following range chart what is the lower control limit for the sample range?
Sample Size / A2 Factor R Chart / D3 Factor R Chart / D4 Factor R Chart2 / 1.83 / 0.00 / 3.27
3 / 1.02 / 0.00 / 2.57
4 / 0.73 / 0.00 / 2.28
5 / 0.58 / 0.00 / 2.11
6 / 0.48 / 0.00 / 2.00
7 / 0.42 / 0.08 / 1.92
8 / 0.37 / 0.14 / 1.86
9 / 0.34 / 0.18 / 1.82
10 / 0.31 / 0.22 / 1.78
11 / 0.29 / 0.26 / 1.74
12 / 0.27 / 0.28 / 1.72
13 / 0.25 / 0.31 / 1.69
14 / 0.24 / 0.33 / 1.67
15 / 0.22 / 0.35 / 1.65
16 / 0.21 / 0.36 / 1.64
17 / 0.20 / 0.38 / 1.62
18 / 0.19 / 0.39 / 1.61
19 / 0.19 / 0.40 / 1.60
20 / 0.18 / 0.41 / 1.59
21 / 0.17 / 0.43 / 1.58
22 / 0.17 / 0.43 / 1.57
23 / 0.16 / 0.44 / 1.56
24 / 0.16 / 0.45 / 1.55
25 / 0.15 / 0.46 / 1.54
Answer:
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