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Taguchi Loss Function Calculator

Work out taguchi loss function instantly with clear inputs, formula shown and shareable results.

About Taguchi Loss Function Calculator

Taguchi's quadratic loss function says quality loss rises with the square of deviation from target: L = k(y - m)^2, with k calibrated so that loss at the tolerance limit equals a known cost. It replaces goalpost thinking — anything inside tolerance is fine — with continuous pressure towards the target.

Formula

Taguchi loss

k = A / tolerance^2; L(y) = k x (y - target)^2

Worked example

With the default values below, Taguchi Loss Function Calculator returns Quality Loss of $144.000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Target Valueminimum -1,000,000,000
50
Tolerance (half-width)minimum 0
0.5
Loss At Tolerance Limitminimum 0.01
400
Actual Measured Valueminimum -1,000,000,000
50.3

Results

Quality Loss
$144.000
Loss Coefficient k
1,600.0000
Deviation From Target
0.30000
Loss Relative To Limit Loss
36.000%

Step by step

  1. 1Values used
  2. 2Taguchi loss
  3. 3Quality Loss= 144.000
  4. 4Loss Coefficient k= 1,600.0000
  5. 5Deviation From Target= 0.30000
  6. 6Loss Relative To Limit Loss= 36.000

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why is loss non-zero inside tolerance?

Because a part at the edge of tolerance performs worse in the customer's assembly than one on target, even though both pass inspection. Stack-up of near-limit parts is where field failures originate.

How is the loss at the tolerance limit estimated?

From the cost of the consequence — scrap, rework, warranty or customer dissatisfaction — at the point where the characteristic is just unacceptable.

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