A quality characteristic has a manufacturing specification (in cm) of 0.20 ± 0.05. Historical data indicate that if the quality characteristic takes on values larger than 0.25 cm or smaller than 0.15 cm, the product fails and a cost of $75 is incurred. Based on this data, answer the question below. The Taguchi loss function is _____. A) L(x) = 75 (x - 0.05)² B) L(x) = 30,000 (x - 0.20)² C) L(x) = 30,000 (0.15 − 0.25)² D) L(x) = 1,500 (0.15 − 0.25)²

Question

Quizplus · Accepted Answer

The Taguchi loss function is given by L(x) = k(x - T)^2, where k is the cost of deviation from the target value T. In this case, the target value is 0.20 cm.

If x ≤ 0.15 or x ≥ 0.25, then the cost is $75. Therefore, k = 75/(0.05)^2 = 30,000.

Thus, the Taguchi loss function is L(x) = 30,000 (x - 0.20)^2.

None of the other options match this expression, so the answer is B.

A Quality Characteristic Has a Manufacturing Specification (In Cm) of 0.20