Concept explainers
To determine: The difference shown by the second set of sample from the first one.
Introduction
Company TT is a division of company DM. It was about to launch a new product. Ms. MY, the
Table 1
Sample | Mean | Range |
1 | 45.01 | 0.85 |
2 | 44.99 | 0.89 |
3 | 45.02 | 0.86 |
4 | 45 | 0.91 |
5 | 45.04 | 0.87 |
6 | 44.98 | 0.9 |
7 | 44.91 | 0.86 |
8 | 45.04 | 0.89 |
9 | 45 | 0.85 |
10 | 44.97 | 0.91 |
11 | 45.11 | 0.84 |
12 | 44.96 | 0.87 |
13 | 45 | 0.86 |
14 | 44.92 | 0.89 |
15 | 45.06 | 0.87 |
16 | 44.94 | 0.86 |
17 | 45 | 0.85 |
18 | 45.03 | 0.88 |
Quiet disappointed with the end results, the manager was figuring out ways to improve the process and free the capital expenditure of $10,000. A former professor suggested going for more samples with less sample sizes. JM conducted the analysis on 27 samples of 5 observations each and the results are tabulated below:
Table 2
Sample | Mean | Range |
1 | 44.96 | 0.42 |
2 | 44.98 | 0.39 |
3 | 44.96 | 0.41 |
4 | 44.97 | 0.37 |
5 | 45.02 | 0.39 |
6 | 45.03 | 0.4 |
7 | 45.04 | 0.39 |
8 | 45.02 | 0.42 |
9 | 45.08 | 0.38 |
10 | 45.12 | 0.4 |
11 | 45.07 | 0.41 |
12 | 45.02 | 0.38 |
13 | 45.01 | 0.41 |
14 | 44.98 | 0.4 |
15 | 45 | 0.39 |
16 | 44.95 | 0.41 |
17 | 44.94 | 0.43 |
18 | 44.94 | 0.4 |
19 | 44.87 | 0.38 |
20 | 44.95 | 0.41 |
21 | 44.93 | 0.39 |
22 | 44.96 | 0.41 |
23 | 44.99 | 0.4 |
24 | 45 | 0.44 |
25 | 45.03 | 0.42 |
26 | 45.04 | 0.38 |
27 | 45.03 | 0.4 |
Answer to Problem 2.2CQ
Explanation of Solution
Given information:
Table 3
Sample | Mean | Range |
1 | 45.01 | 0.85 |
2 | 44.99 | 0.89 |
3 | 45.02 | 0.86 |
4 | 45 | 0.91 |
5 | 45.04 | 0.87 |
6 | 44.98 | 0.9 |
7 | 44.91 | 0.86 |
8 | 45.04 | 0.89 |
9 | 45 | 0.85 |
10 | 44.97 | 0.91 |
11 | 45.11 | 0.84 |
12 | 44.96 | 0.87 |
13 | 45 | 0.86 |
14 | 44.92 | 0.89 |
15 | 45.06 | 0.87 |
16 | 44.94 | 0.86 |
17 | 45 | 0.85 |
18 | 45.03 | 0.88 |
Formula:
Mean Chart:
Difference shown by the second set of sample from the first one:
Date set:1
Table 4
Sample | Mean | Range |
1 | 45.01 | 0.85 |
2 | 44.99 | 0.89 |
3 | 45.02 | 0.86 |
4 | 45 | 0.91 |
5 | 45.04 | 0.87 |
6 | 44.98 | 0.9 |
7 | 44.91 | 0.86 |
8 | 45.04 | 0.89 |
9 | 45 | 0.85 |
10 | 44.97 | 0.91 |
11 | 45.11 | 0.84 |
12 | 44.96 | 0.87 |
13 | 45 | 0.86 |
14 | 44.92 | 0.89 |
15 | 45.06 | 0.87 |
16 | 44.94 | 0.86 |
17 | 45 | 0.85 |
18 | 45.03 | 0.88 |
45 | 0.872777778 |
Excel worksheet:
From factors of three-sigma chart, for n=20, A2 = 0.18; D3 = 0.41; D4 = 1.59
Mean control chart:
Range control chart:
Upper control limit:
The upper control limit is calculated by adding the product of 0.18 and 0.873 with 45, which yields 45.156.
Lower control limit:
The lower control limit is calculated by subtracting the product of 0.18 and 0.873 with 45, which yields 44.842.
A graph is plotted using the UCL, LCL and samples values.
Diagram 1
Date set: 2
Table 5
Sample | Mean | Range |
1 | 44.96 | 0.42 |
2 | 44.98 | 0.39 |
3 | 44.96 | 0.41 |
4 | 44.97 | 0.37 |
5 | 45.02 | 0.39 |
6 | 45.03 | 0.4 |
7 | 45.04 | 0.39 |
8 | 45.02 | 0.42 |
9 | 45.08 | 0.38 |
10 | 45.12 | 0.4 |
11 | 45.07 | 0.41 |
12 | 45.02 | 0.38 |
13 | 45.01 | 0.41 |
14 | 44.98 | 0.4 |
15 | 45 | 0.39 |
16 | 44.95 | 0.41 |
17 | 44.94 | 0.43 |
18 | 44.94 | 0.4 |
19 | 44.87 | 0.38 |
20 | 44.95 | 0.41 |
21 | 44.93 | 0.39 |
22 | 44.96 | 0.41 |
23 | 44.99 | 0.4 |
24 | 45 | 0.44 |
25 | 45.03 | 0.42 |
26 | 45.04 | 0.38 |
27 | 45.03 | 0.4 |
44.9959 | 0.40111 |
Excel worksheet:
From factors of three-sigma chart, for n=20, A2 = 0.58
Mean control chart:
Range control chart:
Upper control limit:
The upper control limit is calculated by adding the product of 0.58 and 0.401 with 44.99, which yields 45.229.
Lower control limit:
The lower control limit is calculated by subtracting the product of 0.58 and 0.401 with 44.99, which yields 44.763.
Diagram 2
On comparing Diagrams 1 and 2, it is evident that the second set of data has closer range of changes while the first set of data is scattered and reveals no information about the changes in the process.
Hence, the second sample reveals the changes in the process changes more clearly than the first set of data.
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Chapter 10 Solutions
Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences)
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