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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 + (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

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter11: Data Analysis And Displays
Section: Chapter Questions
Problem 7CR
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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
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
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
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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