Question

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

Answer 1

option (C) L(x) = 200,000(x - 0.40)²

Step-by-step 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