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), if the actual quality characteristic, x, is 0.41? Round final answer to nearest dollar.
A) $25.
B) $100.
C) $10,000.
D) $4,000,000.
E) $4,100,000.

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) , if the actual quality characteristic, x, is 0.41? Round final answer to nearest dollar.

What is the amount of the estimated loss, L(x), using a Taguchi Quality Loss Function (QLF), if the actual quality characteristic, x, is 0.41? Round final answer to nearest dollar.
A) $25.
B) $100.
C) $10,000.
D) $4,000,000.
E) $4,100,000.

Quizplus · Accepted Answer

The Taguchi Quality Loss Function (QLF) estimates the loss associated with deviating from the target value. The formula for the quadratic loss function is L(x) = k(x - T)^2, where L(x) is the loss associated with a deviation, x is the actual value, T is the target value, and k is a constant calculated based on the maximum loss (K) at the tolerance limit. Given that the tolerance is ±0.010 from the target of 0.400 and the maximum loss (cost for warranty repair or replacement) is $100 when the deviation equals the tolerance, we can find k using the formula K = k(tolerance)^2. Here, K = $100 and the tolerance = 0.010, so k = $100 / (0.010)^2 = $100 / 0.0001 = $1,000,000. For x = 0.41, the deviation from the target (0.400) is 0.01. Thus, L(x) = $1,000,000 * (0.01)^2 = $1,000,000 * 0.0001 = $100.

Ladder Manufacturing Specifies the Quality Characteristic of One of Its