Question

A critical part has a manufacturing specification (in cm) of 0.325 ± 0.010. Based on this information, if this measurement is larger than 0.335 or smaller than 0.315, the product fails at a cost of $120. Determine the Taguchi loss function in the given scenario.

Answer 1

Step-by-step explanation:

Manufacturing specification

0.325 ± 0.010 I'm

The quality characteristic is 0.325

Functional tolerance is $120

The lost function is given

λ = C (x—t)²

Where, C is a constant

t is quality characteristic

And x is target value

Constant’ is the coefficient of the Taguchi Loss, or the ratio of functional tolerance and customer loss.

Then, C= tolerance / loss²

Measurement loss is

Loss = 0.335-0.315

Loss =0.01cm

Therefore,

C = 120/0.01²

C = 1,200,000

λ = C (x —t)²

λ = 1,200,00 (x—0.325)²

Answer 2

`L(y)=12* 10^(5)(y-0.325)^2`

Step-by-step explanation:

We know that Taguchi loss function given as

`L(y)=k(y-m)^2`

Where L is the loss when quality will deviate from target(m) ,y is the performance characteristics and k is the quality loss coefficient.

Given that 0.325±0.010 ,Here over target is m=0.325 .

When y=0.335 then L=$120,or when y=0.315 then L=$120.

Now to find value of k we will use above condition

`L(y)=k(y-m)^2`

`120=k(0.335-0.325)^2`

`k=12* 10^(5)`

So Taguchi loss function given as

`L(y)=12* 10^(5)(y-0.325)^2`