# Statistics

Multivariate Analysis – Final Assignment

·

·
Ensure that all steps are documented in an appropriate order, including output obtained from calculation performed using Minitab.

Question

1

(15 marks)

A company needs to enhance their measurement system accuracy. Seven inspectors were selected to measure the length of three parts twice.

Use the
MSA data file to perform the following:

A. Perform Gauge R & R study and provide your conclusion on the results.

B. Provide your recommendation to improve the measurement system accuracy.

C. Provide the best estimate for each part length.

Question 2 (15 marks)

A car rental agency is trying to study the relationship between car speed (km/hour) and the fuel consumption (kilometer per liters).

Use the
Fuel Consumption data sheet to perform the following tasks:

A. Study the relationship between fuel consumption per kilometer and the car speed using scatter diagram and correlation coefficient.

B. Develop a mathematical equation to predict the fuel consumption per kilometer using car speed.

C. Develop your conclusion based on the studied relationship.

E. Predict the car fuel consumption, if the car speed is 100 km/hour.

Question 3 (15 marks)

Your trip between home and office may be conducted through 2 different roads using Uber service or your private car.

Use
Trip Duration Data to perform the following:

A. Draw Multi-Vari chart.

Question 4 (15 marks)

You wish to evaluate supplier using 4 criteria:

1. Price.

2. On time delivery

3. Quality of product

4. Responding to emergency changes in order

Use
Supplier Data to perform the following tasks.

A. Use Analytic Hierarchy Process to determine the weight of each criterion.

C. Select the best supplier.

Question 5 (15 marks)

A customer survey was conducted to evaluate consumer satisfaction for 3 products.

Use the
Customer Survey Sheet provided to perform the following tasks:

A. Check if customer satisfaction of Product A is significantly less than 3.

B. Check if there is a significant difference between Product A & Product B customer satisfaction.

C. Check if there is a significant difference between Product B & Product C customer satisfaction.

Question 6 (15 marks)

Data was collected from manufacturing plant to study several factors affecting labor production. These factors are:

· Training Hours of each Labor,

· Labor Age,

· Weather Temperature,

· Labor Years of Experience,

· Shift Number.

Use the
Labor Production Data Sheet to perform the following tasks:

A. Develop a mathematical equation to predict the labor production using all factors.

B. Provide your comments on the prediction accuracy of the previous equation.

C. Develop a mathematical equation to predict the labor production using two factors only.

D. Provide your comments on the prediction accuracy of the previous equation.

Question 7 (10 marks)

A call center needs to optimize usage of resources. Usually, the call duration ranges between 1.3 to 3.7 minutes to receive a customer request. Call duration depends on 3 factors:

· Call agent experience (Moderate or High),

· Type of customer request (Simple or Complex)

· System used by the call agent to record request (Manual or Automated)

A. Establish a Full Factorial Design for the above mentioned case, using one replicate without center point.

B. How many runs we need to perform, if we decided to conduct Half Factorial.

C. What is your conclusion on the resolution of the previous Half Factorial design?

1

2

>MS

A

Data

A

1

1

8

2
A

2
B

2
C

3
A

3
B
1

3
C
138

4
A

4
B

4
C

5
A

5
B

5
C
1

6
A
148

6
B
137

6
C
139

7
A

7
B

7
C
149

1
A

1
B
137

1
C
138

2
A
148

2
B
137

2
C
139

3
A
139

3
B

3
C

4
A
145

4
B
135

4
C

5
A
148

5
B
136

5
C
139

6
A
147

6
B
137

6
C
139

7
A
149

7
B
139

7
C
139

 Inspectors Part Length (mm) 1 1 4 5 B 1 3 8 C 13 14 7 1 37 13 9 1 41 38 1 45 1 34 13 6 1 48 1 35 39 1 49 1 6 0 1 46 1 31 1 47 1 36

## Fuel Consumption

Fuel Consumption

Speed

60

0

45

49

3

3.91
47

6

54

99

106

45

45

53

60

5

106

77

90

74

 Car 3.38 98 5.02 5. 25 68 3.0 4. 12 5. 19 64 5.31 71 4. 33 50 3.05 99 4.76 80 4. 42 72 4.55 54 3.91 88 1. 24 11 5. 29 79 5.13 74 2. 22 10 4. 82 1. 23 1 17 3.19 4. 77 83 2.74 3.57 4. 53 52 5. 20 65 0.25 117 3. 90 4. 43 51 4.54 3.45 89 4.91 2.8 4.60 86 5.23 3.39 1.99 110 5. 15

## Trip Duration

A

Uber
B

Office
Car
A
64

Home
Uber
B

Home
Car
B

Office
Car
B

Office
Car
A
51

Office
Uber
A

Home
Uber
B
82

Office
Uber
A
48

Home
Uber
A
72

Office
Car
B
48

Office
Uber
B
41

Home
Car
B

Home
Car
A
74

Home
Car
A
61

 Destination Method Road Duration (min) Home Uber 73 Office 61 69 75 58 62 66

## Supplier Data

22
10
64
4

4%

Supplier

Delivery Time
Quality
Response

1

Good

2
2
1

2

2

Poor
Poor
Good
1.5

1
1
1

3
15
Poor
Good
Good
3.0

1
1
1
0.78

4
17
Good
Good
Good

2
2
2

5
23
Good
Poor
Good

2
2
2
1.56

6
20
Poor
Poor
Poor

1
1
1
0.78

7
18
Good
Good
Poor
2.3

2
2
2
1.56

8
21
Good

Poor
1.5

2
2
2
1.56

9

Excellent
Good
Poor
2.8

3
3
3

10
16
Good
Excellent
Poor
2.8

2
2
2
1.56

11
21
Poor
Poor
Poor
1.5

12
18
Excellent
Poor
Good
2.3

0.00

13
23
Excellent
Excellent
Good
1.0

14
21
Poor
Good
Poor
1.5

15
22
Excellent
Good
Poor

16
15
Excellent
Good
Good
3.0

17
23
Poor
Poor
Good
1.0

18
19
Excellent
Poor
Poor

19
21
Poor
Good
Poor
1.5

20
15
Poor
Good
Poor
3.0

2.0

3.0

15

1.0

1.0

23

3.0

8

 22% 10% 6 4% Price Delivery Time Quality Response 18 Good Poor 2.3 1.5 21 0.78 2.5 1.56 1.0 1.8 Excellent 16 2.34 0.00 1.3 2.0

## Customer Survey

1
4
0
4

2
1
7
4

3
4
5
1

4
9
8
7

5
1
3
9

6
1
10
2

7
0
4
3

8
4
3
2

9
4
1
5

10
9
2
2

11
3
1
4

12
1
9
2

13
10
0
5

14
6
7
9

15
2
9
6

16
8
2
5

17
8
10
5

18
0
3
6

19
4
7
1

20
7
6
8

21
0
4
2

22
4
3
10

23
0
2
8

24
10
3
0

25
9
7
4

3
7
2

1
6
2

10
5
4

29
10
0
9

1
8
0

31
10
4
5

4
0
6

33
9
3
1

34
8
10
7

35
9
10
8

36
0
6
2

37
9
5
0

38
0
0
3

39
8
5
9

10
4
7

41
0
8
5

42
3
1
8

43
10
1
3

1
2
9

45
6
6
7

46
8
4
6

 Customer ID Product A Product B Product C 26 27 28 30 32 40 44

## Labor Production

2

1

6

6

2

6

2

2

.4

16.4

1

2

34.6

3
120

2
121

16.6

2

1

1
117.2

3
117

81.965
34.07
16.04
9.6
2

3
121.4

77.495
34.32

11.4
1
118

2

1

3
89

2

1

2

11.2
1

18.12

1

2

6.6
2

35.73

2

8.36
2

2

69.715
37.2
16.71
11.2
1
119.8

77.495
34.32
16.62
11.4
1
118

 Training (h) Age (y) Temp. (Co) Experience (y) Shift # Production (kg) 77.495 34.32 1 6.6 11.4 118 74.845 36.5 16.4 11.2 120 68.445 34.6 17.66 13.34 108.4 81.965 34.07 16.04 9.6 121 86.045 35.75 7.15 114.4 87.515 34.46 16.28 7.56 117.2 90.945 16.06 8.42 90.555 35.38 15.93 9.24 75.6 35.85 6.7 104 76.935 35.68 16.41 6.95 108.8 79.35 35.35 16.17 7.69 80.165 35.04 15.92 8.36 121.4 80.855 32.2 16.19 10.56 16.62 71.185 31.08 17.37 13.18 109.2 69.485 35.73 18.12 13.54 103.2 63.81 34.11 18.53 14.31 77.455 34.79 15.54 9.93 126.6 75.79 35.77 15.7 10.63 123.8 75.335 36.44 16.45 11.79 121.6 69.715 37.2 16.71 119.8 66.68 35.07 13.9 102 56.855 35.26 19.05 14.73 82.4 65.31 35.56 16.51 103.4 70.405 16.02 7.52 115.2 70.96 36.46 15.89 119.6 72.69 36.26 15.83 9.33 120.8

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