# Taguchi Loss Function Problem

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#### mikethepenguin

Hi all

I am working for an aerospace company and have an answer to a problem which I have tackled but I can't justify the answer.

The cost of a rework for a manufactured part is ?85 per hour. The part has to be made to the following dimensions 195 +/- 0.04mm. What is the cost if the average part size is 194.13mm? The down time attributed to this part failure is usually 25 hours.

I have used the Taguchi Loss Function found around the web...

k = A/Delta = 85/0.04^2 = ?53125 <-- Huge cost already

L = 53125(194.13 - 195)^2 = ?40210.31

So using this formula it's saying the average part cost per failure outside the specification is ?40210.31 for this raverage.

Using the downtime figure earlier 25 x ?84 = ?2100 is the labour cost attributed to this failure...

How could a person taking this to a business justify this cost? I don't understand...it seems absurd. Have I made a mistake in my calculation?

Elsmar have used standard deviation in their formula but I do not understand why?

Any help will be grateful!!!

#### Miner

##### Forum Moderator
Re: Taguchi Loss Function

The value of the Taguchi Loss function is more conceptual. Rather than trying to justify the actual monies calculated by the formula, focus on the concept that a part made at 194.041 is not radically different from one made at 194.039 yet conventional thinking would say that the former costs a lot in rework or scrap while the latter does not.

The loss function concept shows that the cost of the former is slightly greater than the cost of the latter, which is more logical.

#### Bev D

##### Heretical Statistician
Super Moderator
We must also figure in physics. how do failures occur?

is it a stack-up tolerance? wear? a (non stack-up tolerance) interaction?
when we engineer specifications we typically make a call based on the mechanism of faliure and the probability of failure.

interaction example: I have a Delran rotor holder that goes on a rotor motor shaft. the shaft has an acceptable 'angle' from straightness and the rotor holder has a upper and lower specification for the diameter of the holder that the blood separator fits on. when the shaft has too much 'angle' the rotor wobbles. if the holder is on the small side the separator can fly off the holder. there is an intersection where too much angle AND too small a holder diameter will always cause the holder to fly off. as these two dimensions move away from this overlap point the probability of a holder flying off diminishes to zero. we set the specs for these two things where the probability of separator flying off is less than .00001. Now of course we could get a holder that is too small but it goes on a very straight rotor shaft (simply by chance) and the separator won't fly off. so the actual cost is based on the frequency distribution of these two dimensions.

there is really no 'canned' formula for the Taguchi loss function. the above example doesn't follow a quadratic...