Style Retouche, Inc., produces compact paint pens used to repair small nicks in exterior automotive paint finishes. If the machinery that fills the pens is not completely cleaned between production runs of different colors, the resulting paint will not match the original color intended. Style Retouche estimates that the cost of a mismatched pen that reaches a customer is $40. The company's target for the residual content of the previous color remaining in the machinery is 0.00 parts per million. Using the Taguchi loss function, how does the quality loss for an actual residual content of 0.01 parts per million compare to the quality loss for an actual content of 0.02 parts per million?
A) The quality loss at 0.02 parts per million is twice as large as the quality loss at 0.01 parts per million.
B) The quality loss at 0.02 parts per million is equal to the quality loss at 0.01 parts per million.
C) The quality loss at 0.02 parts per million is four times as large as the quality loss at 0.01 parts per million.
D) The quality loss at 0.02 parts per million is 40 times as large as the quality loss at 0.01 parts per million.

Question

Quizplus · Accepted Answer

The Taguchi loss function is quadratic, meaning the loss increases with the square of the deviation from the target. Therefore, if the deviation doubles (from 0.01 to 0.02), the loss increases by a factor of four.