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. In the given scenario, the Taguchi loss function is correctly represented by which of the following equations ?
A) L(x) = 200 (x - 0.03) 2
B) L(x) = 2,000 (x - 0.43) 2
C) L(x) = 200,00 (x - 0.37) 2
D) L(x) = 200,000 (x - 0.40) 2

Question

Quizplus · Accepted Answer

The Taguchi loss function is given by L(x) = k(x-T)^2, where x is the actual value, T is the target value, and k is a constant that determines the steepness of the function. In this case, the target value is 0.40, and the tolerance is 0.03. Therefore, the loss function should be symmetric around 0.40 and have a steepness that reflects the cost of repair ($180.00). Choice D is the only equation that has the correct target value and is symmetric around it. It also has a steepness that corresponds to the cost of repair, since (0.03)^2 times the constant is close to $180.00. Therefore, D is the best choice.

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