Reference no: EM132314942
Industrial Statistics Lab Assignment -
Note:
1. All questions are compulsory.
2. Solve the following questions in MS Excel.
3. Take the screenshots of the final output/spreadsheet.
4. Paste all screenshots in the assignments booklets with all necessary hypotheses, interpretation, etc.
Q1. A Company uses a process to paint refrigerators with a coat of enamel. During each shift, a sample of 5 refrigerators is selected (2 hours apart) and the thickness of the paint (in mm) is determined. If the enamel is too thin, it will not provide enough protection. If it is too thick, it will result in an uneven appearance with running and wasted paint. In this regards, total 20 subgroups consisting of a sample of 5 refrigerators in each sub group were selected. The following table lists the measurements from 20 consecutive shifts:
|
Shift No.
|
Thickness (in mm)
|
|
1
|
2.4
|
2
|
2.3
|
2.1
|
2.4
|
|
2
|
2.3
|
2.1
|
2.3
|
2
|
2.5
|
|
3
|
2
|
2
|
2.1
|
2.2
|
2.1
|
|
4
|
2.5
|
2
|
2.1
|
2.3
|
2.4
|
|
5
|
2.3
|
2.2
|
2.3
|
1.8
|
2.5
|
|
6
|
1.9
|
2
|
2.4
|
1.9
|
2.3
|
|
7
|
1.9
|
2.3
|
2.1
|
1.7
|
2
|
|
8
|
2.5
|
2.3
|
2.3
|
2.4
|
2.2
|
|
9
|
2.1
|
2.5
|
2.1
|
1.9
|
2
|
|
10
|
2.3
|
2
|
1.7
|
2.2
|
2.1
|
|
11
|
2.8
|
2.7
|
3.2
|
2.5
|
2.7
|
|
12
|
2.1
|
2.5
|
1.9
|
2.6
|
2.2
|
|
13
|
1.8
|
2.9
|
2.2
|
2.3
|
2.5
|
|
14
|
1.9
|
2.5
|
1.8
|
1.9
|
2.1
|
|
15
|
2.1
|
2.7
|
2.2
|
2.2
|
1.7
|
|
16
|
2.8
|
2.3
|
2.3
|
2.5
|
1.8
|
|
17
|
2.6
|
2.1
|
2.6
|
1
|
1.5
|
|
18
|
1.6
|
1.3
|
2.3
|
3
|
3
|
|
19
|
2
|
2.3
|
2.4
|
2.5
|
2.9
|
|
20
|
1.5
|
2.5
|
2
|
1.7
|
2.6
|
The quality manager of this company needs to construct suitable control charts for variability as well as average to infer whether the thickness of paint process is under control or not. If it is out-of-control, construct the revised control charts.
Q2. A company is monitoring the percentage of line items that are shipped correctly from a major supplier. The company's quality people randomly sampled the number of line items shipped each week from the supplier as well as the number of line items shipped correctly. They have collected data for the past 25 weeks. The data are displayed in the following table:
|
Week
|
Number of Shipped Items
|
Number of Correctly Shipped Items
|
|
1
|
86
|
74
|
|
2
|
76
|
76
|
|
3
|
42
|
34
|
|
4
|
94
|
93
|
|
5
|
115
|
115
|
|
6
|
37
|
34
|
|
7
|
79
|
71
|
|
8
|
89
|
83
|
|
9
|
64
|
54
|
|
10
|
60
|
58
|
|
11
|
116
|
115
|
|
12
|
120
|
98
|
|
13
|
46
|
44
|
|
14
|
103
|
102
|
|
15
|
81
|
79
|
|
16
|
126
|
122
|
|
17
|
117
|
102
|
|
18
|
17
|
13
|
|
19
|
64
|
52
|
|
20
|
60
|
59
|
|
21
|
92
|
87
|
|
22
|
104
|
103
|
|
23
|
118
|
103
|
|
24
|
89
|
87
|
|
25
|
77
|
74
|
Construct a suitable control chart for fraction of incorrectly shipped items to check whether the process is said to be in a state of control or not using both approaches. Also construct the revised control charts, if necessary.
Q3. A researcher wants to study the varieties of cigarettes according to their tar, nicotine, and carbon monoxide content as each of these three substances considered hazardous to a smoker's health. The following table presents data on tar, nicotine, and carbon monoxide content (in milligrams) and weight (in grams) for a sample of 25 brand of cigarettes in a recent year:
|
Tar
|
Nicotine
|
Weight
|
Carbon Monoxide
|
|
12.9
|
0.74
|
0.87
|
12.4
|
|
15.2
|
0.94
|
0.98
|
15.4
|
|
28.6
|
1.91
|
1.05
|
22.3
|
|
6.8
|
0.55
|
1.81
|
9
|
|
2.9
|
0.28
|
0.83
|
4.2
|
|
13.8
|
0.92
|
0.77
|
13.8
|
|
7.6
|
0.64
|
0.91
|
7.8
|
|
11.2
|
0.83
|
0.81
|
11.1
|
|
15.4
|
1
|
0.82
|
15.1
|
|
13.7
|
0.9
|
0.77
|
14.2
|
|
12.5
|
0.89
|
0.85
|
11.8
|
|
13.9
|
0.78
|
0.82
|
13.2
|
|
6.6
|
0.45
|
0.86
|
8.8
|
|
10.2
|
0.66
|
1.01
|
9
|
|
7.8
|
0.62
|
0.74
|
8.3
|
|
-0.2
|
0.01
|
0.67
|
0.3
|
|
15.8
|
1.14
|
0.8
|
17.3
|
|
11.6
|
0.96
|
0.92
|
11.4
|
|
14.6
|
0.84
|
0.84
|
16.3
|
|
3.3
|
0.3
|
0.8
|
3.7
|
|
13.3
|
0.89
|
0.89
|
14.7
|
|
6.1
|
0.49
|
0.87
|
7.3
|
|
7.4
|
0.57
|
0.85
|
9.4
|
|
14
|
0.9
|
0.83
|
12.7
|
|
10.8
|
0.7
|
1
|
13.7
|
i) Prepare a scatter plots matrix to get an idea about the relationship among the variables.
ii) Develop the best fitted multiple regression model considering carbon monoxide content as a function of tar content, nicotine content, and weight using stepwise regression procedure.
iii) Does the fitted regression model satisfy the linearity and normality assumptions?
Q4. An amusement park manager wishes to improve the quality and activities based on the total number of kids visited daily. The scheduling will be prepared based on the daily levels of customers in the past 10 weeks. The numbers of kids visited in the park during that period were given below:
|
Week
|
Monday
|
Tuesday
|
Wednesday
|
Thursday
|
Friday
|
Saturday
|
Sunday
|
|
1
|
359
|
524
|
287
|
257
|
460
|
376
|
248
|
|
2
|
195
|
274
|
228
|
293
|
354
|
193
|
318
|
|
3
|
135
|
204
|
265
|
139
|
291
|
124
|
115
|
|
4
|
180
|
259
|
106
|
278
|
339
|
118
|
303
|
|
5
|
120
|
189
|
250
|
124
|
289
|
132
|
308
|
|
6
|
295
|
208
|
333
|
150
|
219
|
280
|
154
|
|
7
|
248
|
157
|
264
|
293
|
168
|
348
|
357
|
|
8
|
237
|
394
|
415
|
394
|
243
|
520
|
345
|
|
9
|
504
|
565
|
439
|
615
|
415
|
485
|
688
|
|
10
|
574
|
764
|
759
|
709
|
667
|
891
|
857
|
i) Determine the seasonal indices for these data using a 7-day moving averages.
ii) Obtain the deseasonalised values.
iii) Fit the appropriate trend for the deseasonalised data using the least-squares method by matrix approach that best describes these data.
iv) Project the number of kids visited on Wednesday of the 52th week.
v) Plot the original data, the deseasonalised data, and the trend.