Ladder Manufacturing specifies the quality characteristic of one of its popular products to be 0.400" ± 0.010. An analysis of company records for the last two years suggests that the average cost for warranty repair or replacement is $100.00 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 Quality Loss Function (QLF), when the actual quality characteristic, x, is 0.405? (Round final answer to nearest dollar.)
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" ± 0.010. An analysis of company records for the last two years suggests that the average cost for warranty repair or replacement is $100.00 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 Quality Loss Function (QLF) , when the actual quality characteristic, x, is 0.405? (Round final answer to nearest dollar.)

What is the amount of the estimated loss, L(x), using a Taguchi Quality Loss Function (QLF), when the actual quality characteristic, x, is 0.405? (Round final answer to nearest dollar.)
A) $25.
B) $5,000.
C) $10,000.
D) $400,000.
E) $405,000.

Quizplus · Accepted Answer

The Taguchi Quality Loss Function (QLF) estimates the loss associated with deviating from the target value. The formula for a symmetric loss function is L(x) = k(x - T)^2, where k is a constant, x is the actual value, T is the target value, and L(x) is the loss. Given that the target is 0.400" and the tolerance is ±0.010, any deviation beyond this tolerance results in a warranty cost of $100. The deviation in this case is 0.005" (0.405 - 0.400). To find k, we use the formula k = Loss / (Deviation)^2 at the tolerance limit. At the tolerance limit of 0.010, the deviation is 0.010 and the loss is $100, so k = $100 / (0.010)^2 = $100 / 0.0001 = $1,000,000. Therefore, the loss for a deviation of 0.005" is L(x) = $1,000,000 * (0.005)^2 = $1,000,000 * 0.000025 = $25.

Ladder Manufacturing Specifies the Quality Characteristic of One of Its