Five (5) things to know about the Taguchi Loss Function:



1. The Taguchi Loss Function (TLF) was developed by Japanese engineer and statistician Genichi Taguchi, who is also known for his contributions to robust design and Taguchi experiments.


2. The TLF states that a deviation of the quality characteristic from its Target value (x-Target) or delta-x, incurs a loss proportional to the square of the deviation:


Loss = k*(x - Target)^2


k = constant, sometimes called the Taguchi loss coefficient

x = actual value of the quality characteristic

Target = target value of the quality characteristic


3. For products with an upper/lower spec limit and Target value in the middle, we can solve for the constant (k) by setting the TLF equal to the product scrap cost at the spec limit (assuming no re-work is possible so that the part needs to be scrapped if outside the spec value). If we do this, the expression for the constant is:

k = 4∙Scrap$ / (Tolerance)^2


The units of k are $/(unit of Tolerance)^2.


The Taguchi Loss is then:


Loss={4*Scrap$*(x - Target)^2} / (Tol^2)


Tightening a tolerance by half increases the loss by 400%! Whereas an improved design with 2X the original tolerance reduces the loss by 1/4th.


4. The TLF makes clear centering a manufacturing process reduces losses much more than reducing the variation of a process way off-center.


5. Taguchi also proposed Loss Functions for Smaller the Better and Larger the Better Quality Characteristics.

  • When the Target value is zero or a minimum (e.g. impurities), Taguchi proposed the following:

Loss = k*x^2


  • Similarly, when the Target value is to be as large as possible (e.g. material strength) the loss is given by:

Loss = k / x^2.


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