Question

A quality characteristic of new iPhone X made at the Amsterdam plant at Apple Computers has a manufacturing specification (in mm) of 0.200 +/- .07. Historical data     indicates that if the quality characteristic takes on values greater than 0.27 or smaller than 0.13 the component fails at a cost of 20.19. Based on these data:

1. determine the Taguchi Loss Function (must show work)
2. calculate an estimated loss for a quality characteristic of .30
3. calculate an estimated loss for quality characteristic of .40.

Answer 1

This is a simple problem related to derivation of taguchi loss functino and its asosciated concepts .

Let us first of all try to understand as to what is a taguchi loss function .

A taguchi loss function is defined as  a way to show how each non-perfect part produced, resultsin a loss for the company and is given mathematically as

where L =cost of rejection (loss or simply loss function) , K=A constant dependent on production parameters, y= Measured value of quality characteristic, yo=Target value of quality characteristic

Now since we have an understanding of taguchi loss function ow, let us try to derive it for our problem .

In our problem it is said that the specification should be 0.200+/- 0.07 or in other words in the range of (0.193,0.207)

Now from the data above we understand that we have to target the value of 0.200 and can have a tolerance of 0.07 to play with.

Thus the taguchi loss fuction

Now lets try to find the constant K

To do so lets look at other given data

it says that the cost of failure (loss cost) is 20.19 when the material goes outside the specification limits of (0.13,0.27)

in other words if y =LSL/USL or ourside it ,L =20.19

keeping values,

20.19=K*(0.200=/-0.07-0.200)²

20.19=K(0.07)²

or, K =20.19/(0.07)²

or, K =4120.408

Keeping this in our original loss function equation we get

L =4120.408*(y-0.200)²

Or, L =4.120*10³*(y-0.200)²

^Or,

b). Now what will be the loss when y =0.30

We simply need to keep y =0.30 in our loss function equation

Thus

L =4.120*10³*(0.300-0.200)²

=41.20

c) when y =0.40

then

L =4.120*10³*(0.400-0.200)²

=164.80