Quality loss function

The quality loss function models quality cost as rising with the square of any deviation from the target specification, L = k(x − T)², not only once a unit falls outside a tolerance limit.

FrameworkTaguchi methods

What it is

See it move

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A component's target diameter is 50 mm, with a known cost of €18 for a 3 mm deviation, fixing k at €18 ÷ 3² = €2 per mm². A 1 mm deviation still costs €2 × 1² = €2, and a 2 mm deviation costs €2 × 2² = €8 — four times as much for only double the deviation, because the relationship is squared.

The formula

LaTeX

L = k(x - T)^2

Variables

$L$: Quality loss per unit (€)
$k$: Cost coefficient (€/mm²)
$x$: Actual measured value (mm)
$T$: Target value (mm)

Estimates the cost of a unit's deviation from its exact target specification, growing with the square of the deviation.

LaTeX

k = \frac{L_0}{d_0^2}

Variables

$L_{0}$: Known loss at the reference deviation (€)
$d_{0}$: Reference deviation from target (mm)

Calibrates k from one observed data point — a known rework or failure cost at a known deviation from target.