# 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 Δx, incurs a loss proportional to the square of the deviation:

**k** = a 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 a 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:

The units of **k** are $/(unit of Tolerance)^2. The Taguchi Loss can then be expressed as:

By inspection, we can see that tightening a tolerance by half *increases* the loss by 400%! Whereas, an improved design with a tolerance 2X as wide *reduces* the loss for a given x by 1/4th.

*Example*

*Say the scrap costs for a given part if it falls outside the tolerance is $10, the tolerance is 0.010 inches, and the deviation from the target value for a particular part (Δx) is 0.0025 inches. The Taguchi loss for this part is:*

*Decreasing the tolerance to one half its prior value (i.e., 0.005 inches) results in a loss of $10.00. Increasing the tolerance to 2X its original value (0.020 inches) decreases the loss for the same part to only $0.625!*

*- The assumption here, of course, is that the part remains functional for the tolerances above.*

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

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

**Smaller the Better:**when the Target value is zero or a minimum (for example, impurities), Taguchi proposed the following:

**Larger the Better:**when the Target value is to be as large as possible (e.g. material strength) the loss is given by:

**If you want to go deeper and find out 3 reasons WHY Taguchi chose a squared loss function, click on this post:** ** 3-Reasons-Taguchi**.