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 0.03 on either side, the product will require a $180 repair. In the given scenario, the Taguchi loss function is correctly represented by which of the following equations? (A) L (x) = 2,000 (x - 0.43) 2 (B) L (x) = 200,00 (x - 0.37) 2 (C) L (x) = 200,000 (x - 0.40) 2 (D) L (x) = 200 (x - 0.03) 2

option (C) L (x) = 200,000 (x - 0.40) ²

Explanation:

Given:

quality characteristic = 0.40

Tolerance = 0.03

Repair cost = $180

Now,

Taguchi loss function is given as:

Loss (in $) = Constant * (Quality characteristic - Target value) ²

For quality characteristic of 'x' target value 't'

and constant A

L (x) = A * (x - t) ²

substituting the given values, we get

$180 = A * (0.03) ² [x - t = tolerance]

or

$180 = A * 0.0009

or

A = 200,000

Hence,

Taguchi loss function

L (x) = 200,000 (x - 0.40) ²

Hence,

the correct answer is option (C) L (x) = 200,000 (x - 0.40) ²