Ladder Manufacturing specifies the quality characteristic of one of its popular products to be 0.400" $\pm$ 0.010.An analysis of company records for the last two years suggests that the average cost for warranty repair or replacement is $100 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 0.400,by the tolerance of 0.010.What is the amount of the estimated loss,L(x),using a Taguchi loss function,when the actual quality characteristic,x,is 0.405?
A)$25.
B)$5,000.
C)$10,000.
D)$400,000.
E)$405,000.

Question

Ladder Manufacturing specifies the quality characteristic of one of its popular products to be 0.400"  $\pm$ 0.010.An analysis of company records for the last two years suggests that the average cost for warranty repair or replacement is $100 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 0.400,by the tolerance of 0.010.What is the amount of the estimated loss,L(x),using a Taguchi loss function,when the actual quality characteristic,x,is 0.405?
A)$25.
B)$5,000.
C)$10,000.
D)$400,000.
E)$405,000.

Quizplus · Accepted Answer

The Taguchi loss function is given by:$$L(x) = k(x - m)^2$$where:* k is a constant* x is the actual quality characteristic* m is the target quality characteristicIn this case, we are given that:* m = 0.400* x = 0.405* k = 100So, the loss function becomes:$$L(x) = 100(0.405 - 0.400)^2 = 25$$Therefore, the estimated loss is $25.

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

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