A quality characteristic has a specification (in cm) of 0.40 ± 0.03. If the value of the quality characteristic exceeds 0.40 by the tolerance of 0.030 on either side, the product will require a $180.00 repair. What is the appropriate Taguchi loss function? A) L(x) = 200,000 (0.43 − 0.37)² B) L(x) = 2,000 (0.43 − 0.37)² C) L(x) = 200 (0.43 − 0.37)² D) L(x) = 200,000 (x − 0.40)²

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The appropriate Taguchi loss function is given as L(x) = C(x − T)^2, where C is the cost of the repair and T is the target value. Here, C = $180.00 and T = 0.40. So, substituting these values, we get L(x) = 180(x − 0.40)^2. However, we need to convert the specification tolerance into a standard deviation using S = Tolerance/6. Here, S = 0.03/6 = 0.005. So, the appropriate loss function becomes L(x) = 180(x − 0.40)^2 + 200,000(0.43 − 0.37)². Simplifying this expression, we get L(x) = 200,000(x − 0.40)², which is Option D.

A Quality Characteristic Has a Specification (In Cm) of 0