Pandra Manufacturing specifies the quality characteristic of one of its popular products to be 0.500" $\pm$0.020.An analysis of company records for the last two years suggests that the average cost for warranty repair or replacement is $125 per unit.The customer service manager believes that the product is likely to fail during the warranty period when the quality characteristic exceeds on either side of the target of 0.500,by the tolerance of 0.020.Using a Taguchi loss function for this company,what is the amount of the estimated loss when the actual quality characteristic,x,is 0.505?
A)$0.3906.
B)$7.8125.
C)$19.53125.
D)$125.000.
E)$1,562.50.

Question

Pandra Manufacturing specifies the quality characteristic of one of its popular products to be 0.500"  $\pm$0.020.An analysis of company records for the last two years suggests that the average cost for warranty repair or replacement is $125 per unit.The customer service manager believes that the product is likely to fail during the warranty period when the quality characteristic exceeds on either side of the target of 0.500,by the tolerance of 0.020.Using a Taguchi loss function for this company,what is the amount of the estimated loss when the actual quality characteristic,x,is 0.505?
A)$0.3906.
B)$7.8125.
C)$19.53125.
D)$125.000.
E)$1,562.50.

Quizplus · Accepted Answer

The Taguchi loss function is $ L(x) = k(x - T)^2 $, where $ k = \frac{C}{\Delta^2} $. Here, $ C = 125 $, $ \Delta = 0.020 $, and $ T = 0.500 $. First, calculate $ k = \frac{125}{0.020^2} = 312,500 $. Then, calculate the loss when $ x = 0.505 $: $ L(0.505) = 312,500 \times (0.505 - 0.500)^2 = 312,500 \times 0.000025 = 7.8125 $.

Pandra Manufacturing Specifies the Quality Characteristic of One of Its ±\pm±

Pandra Manufacturing Specifies the Quality Characteristic of One of Its $\pm$