Heiderberg Manufacturing specifies the quality characteristic for one of its key components to be 154" $\pm$ 4.The cost of failure is estimated to be $8,000 per unit.Using the Taguchi Loss Function the firm has estimated the loss,L(x),at the quality characteristic that the firm has experienced,x,to be $4,500.What is the estimated loss if the deviation from the value of the quality characteristic doubled?

Question

Heiderberg Manufacturing specifies the quality characteristic for one of its key components to be 154"  $\pm$ 4.The cost of failure is estimated to be $8,000 per unit.Using the Taguchi Loss Function the firm has estimated the loss,L(x),at the quality characteristic that the firm has experienced,x,to be $4,500.What is the estimated loss if the deviation from the value of the quality characteristic doubled?

Quizplus · Accepted Answer

First, we need to use the Taguchi Loss Function formula to find the loss coefficient:

L(x) = k(x - T)^2

where: 
- k = cost of poor quality per unit 
- x = actual quality value 
- T = target quality value

Given that L(x) = $4,500, k = $8,000, and T = 154", we can solve for x:

$4,500 = $8,000(x - 154")^2 
(x - 154")^2 = 0.5625 
x - 154" = ±0.75 
x = 154" ± 0.75

So the actual quality value is either 153.25" or 154.75".

Next, we need to find the loss coefficient for the doubled deviation from the target quality value:

L(x) = k(x - T)^2 
L(154" ± 1.5) = $8,000(154" ± 1.5 - 154")^2 
L(152.5") = L(155.5") = $4,000

Therefore, the estimated loss if the deviation from the value of the quality characteristic doubled would be $4,000.

Heiderberg Manufacturing Specifies the Quality Characteristic for One of Its ±\pm±

Heiderberg Manufacturing Specifies the Quality Characteristic for One of Its $\pm$