Q4. A manufacturer of tennis rackets intends to set 45 lb tension in one of its product lines. The company spends £60,000 for total warranty (merchandise returned for out of specification tension). A sample data from monthly production of 32000 rackets show the following readings: 45 50 54 46 47 48 (unit: lb) To improve the product, the owner invested £220,000 in a new assembly operation which produced the following samples: 43 46 45 44 45 44.5 (unit: lb) a) Using Taguchi loss function to calculate how much saving the investment has produced, using Lav = k· MSD ≈ k[s² + (ỹ − m)²], where Lap is the average Taguchi loss; MSD is the Mean Squared Deviation; k is the constant in Taguchi loss function. b) Perform a t-test to see if there is a significant difference in quality due to two different assembly operations (significance level a=0.05) (t-distribution table attached in Fig. Q4 below). The t-test statistic is given by: G₁-3₂)-De FEA where (n-1)+(₂-1) s] m+m₂-2
Q4. A manufacturer of tennis rackets intends to set 45 lb tension in one of its product lines. The company spends £60,000 for total warranty (merchandise returned for out of specification tension). A sample data from monthly production of 32000 rackets show the following readings: 45 50 54 46 47 48 (unit: lb) To improve the product, the owner invested £220,000 in a new assembly operation which produced the following samples: 43 46 45 44 45 44.5 (unit: lb) a) Using Taguchi loss function to calculate how much saving the investment has produced, using Lav = k· MSD ≈ k[s² + (ỹ − m)²], where Lap is the average Taguchi loss; MSD is the Mean Squared Deviation; k is the constant in Taguchi loss function. b) Perform a t-test to see if there is a significant difference in quality due to two different assembly operations (significance level a=0.05) (t-distribution table attached in Fig. Q4 below). The t-test statistic is given by: G₁-3₂)-De FEA where (n-1)+(₂-1) s] m+m₂-2
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![Q4.
A manufacturer of tennis rackets intends to set 45 lb tension in one of its product
lines. The company spends £60,000 for total warranty (merchandise returned for out
of specification tension). A sample data from monthly production of 32000 rackets
show the following readings:
45 50 54 46 47
48 (unit: lb)
To improve the product, the owner invested £220,000 in a new assembly operation
which produced the following samples:
43
46
45 44
45
44.5 (unit: lb)
a) Using Taguchi loss function to calculate how much saving the investment has
produced, using Lav = k· MSD ≈ k[s² + (5 m)²], where Lap is the average
Taguchi loss; MSD is the Mean Squared Deviation;k is the constant in Taguchi
loss function.
b)
Perform a t-test to see if there is a significant difference in quality due to two
different assembly operations (significance level a=0.05) (t-distribution table
attached in Fig. Q4 below). The t-test statistic is given by:
(3₁-3₂)-Da
(+9)
where -(n-1)²+(n₂-1) s
m+m₂-2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F904b75ff-cdd4-43ab-971d-8cd569ae478b%2Fa252f819-a6f1-48e2-9d47-4aa885787531%2Fo1lrvt8_processed.png&w=3840&q=75)
Transcribed Image Text:Q4.
A manufacturer of tennis rackets intends to set 45 lb tension in one of its product
lines. The company spends £60,000 for total warranty (merchandise returned for out
of specification tension). A sample data from monthly production of 32000 rackets
show the following readings:
45 50 54 46 47
48 (unit: lb)
To improve the product, the owner invested £220,000 in a new assembly operation
which produced the following samples:
43
46
45 44
45
44.5 (unit: lb)
a) Using Taguchi loss function to calculate how much saving the investment has
produced, using Lav = k· MSD ≈ k[s² + (5 m)²], where Lap is the average
Taguchi loss; MSD is the Mean Squared Deviation;k is the constant in Taguchi
loss function.
b)
Perform a t-test to see if there is a significant difference in quality due to two
different assembly operations (significance level a=0.05) (t-distribution table
attached in Fig. Q4 below). The t-test statistic is given by:
(3₁-3₂)-Da
(+9)
where -(n-1)²+(n₂-1) s
m+m₂-2
Transcribed Image Text:Degrees .005 (1-tail)
01 (2-tails)
of
Freedom
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
82
28
29
63.657
9.925
5.841
4.604
4.032
3.707
3.500
3.355
3.250
3.169
3.106
3.054
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.831
2.819
2.807
2.797
2.878
2.779
2.771
2.763
2.756
Large 2.575
Significance level = Q
01 (1-tail) .025 (1-tail) .05 (1-tail)
.02 (2-tails) .05 (2-tails)
.10 (2-tails)
31.821
6.965
4.541
3.747
3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.625
2.602
2.584
2.567
2.552
2.540
2.528
2.518
2.508
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.327
12.706
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.132
2.120
2.110
2.101
2.093
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.052
2.048
2.045
1.960
Fig. Q4
6.314
2.920
2.353
2.132
2.015
1.943
1.895
1.860
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
1.701
1.699
1.645
.10 (1-tail)
.20 (2-tails)
3.078
1.886
1.638
1.533
1.476
1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
1.333
1.330
1.328
1.325
1.323
1.321
1.320
1.318
1.316
1.315
1.314
1.313
1.311
1.282
.25 (1-tail)
50 (2-tails)
1.000
.816
.765
.741
.727
.718
.711
.706
.703
.700
.697
.696
.694
.692
.691
.690
.689
.688
.688
.687
.686
.686
.685
.685
.684
.684
.684
.683
.683
.675
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