# Taguchi Loss Function Calculator (Cost of Being Off Target) > Source: https://netray.co/tools/taguchi-loss-function-calculator > Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems. > Section: Free Tools ## Short answer Put a cost on variation and off-centre running using the quadratic loss L = k (y - T)^2, and see what centring on target is worth. ## Category quality ## Industry Discrete Manufacturing ## Audience - Quality engineer - Process engineer - Manufacturing engineer ## Tool **Kind:** calculator **Currency:** $ **Inputs:** #### Target value (T) **Key:** target **Type:** number **Default:** 50 **Step:** 0.01 #### Process mean **Key:** mean **Type:** number **Default:** 50.2 **Step:** 0.01 #### Process standard deviation **Key:** sd **Type:** number **Default:** 0.15 **Min:** 0 **Step:** 0.01 #### Tolerance half-width (delta) **Key:** delta **Type:** number **Default:** 0.5 **Min:** 0.0001 **Step:** 0.01 **Help:** Distance from target to a spec limit. #### Cost at the spec limit (A0) **Key:** a0 **Type:** number **Default:** 12 **Min:** 0 **Step:** 0.5 **Unit:** $ per unit **Help:** Average cost of scrap, rework or customer loss for a unit right at the limit. #### Annual volume **Key:** volume **Type:** number **Default:** 200000 **Min:** 0 **Step:** 1000 **Unit:** units **Outputs:** #### Loss coefficient k (A0 / delta^2) **Key:** k **Expr:** a0 / (delta * delta) **Format:** decimal #### Average loss per unit **Key:** loss_u **Expr:** k * (sd * sd + pow(mean - target, 2)) **Format:** currency **Primary:** true #### Loss per unit if centred **Key:** loss_c **Expr:** k * sd * sd **Format:** currency #### Annual loss **Key:** annual **Expr:** loss_u * volume **Format:** currency **Primary:** true #### Annual saving from centring **Key:** save_c **Expr:** (loss_u - loss_c) * volume **Format:** currency #### Saving if sigma halved **Key:** save_v **Expr:** k * (sd * sd - sd * sd / 4) * volume **Format:** currency **Chart:** #### Loss per unit as the mean moves **Type:** line **X:** mean **From:** 49.5 **To:** 50.5 **Steps:** 21 **Series:** - loss_u **Disclaimer:** A planning model. A0 is an estimate and the quadratic form is an approximation of customer loss near the target. ## Content **Intro:** A part just inside the tolerance is not as good as one on target, even though go/no-go inspection treats them the same. The Taguchi loss function gives that difference a dollar value. Use it to justify centring a process or cutting variation before the parts become scrap. **Sections:** #### How to use it **Body:** Enter the target, the current process mean and standard deviation, and the half-width of the tolerance. Estimate A0, the average cost when a unit sits exactly at a specification limit, from scrap cost, rework cost and warranty or field cost. Add annual volume. The results show the average loss per unit, the yearly total, and the value of centring on target or halving the standard deviation. **Bullets:** - Estimate A0 with finance or cost accounting - Use the same units for target, mean, sigma and delta - Compare against the cost of a process improvement #### The formula **Body:** For a nominal-is-best characteristic, the loss for one unit with value y is L = k (y - T)^2, where k = A0 / delta^2. Averaged over a population with variance sigma^2 and mean shifted by (mean - T), the expected loss is k x (sigma^2 + (mean - T)^2). This shows two separate levers: the bias term is removed by centring, and the variance term only by reducing variation. The tool computes both and the saving from each. #### Worked example **Body:** With a tolerance of plus or minus 0.50, A0 of $12 and a mean 0.20 high, k is 48. Expected loss per unit is 48 x (0.0225 + 0.04), about $3.00, or $600,000 a year at 200,000 units. Centring leaves 48 x 0.0225, about $1.08 per unit. Most of the loss here is bias, and the chart shows the quadratic shape, so even a small shift costs more than it looks. #### Common mistakes **Body:** The biggest uncertainty is A0; a guess that is twice too high doubles every result, so show a range. The method also does not apply to smaller-is-better or larger-is-better characteristics without a modified formula. Do not treat the output as an accounting number; it estimates the customer's and your own loss together. Use it to rank projects and argue for tighter targets, not to book savings. **Cta:** If you want variation tracked against target per part number from your ERP quality data, we can help scope a private report. **Faq:** #### What is the Taguchi loss function? **Answer:** It is a quadratic model that says quality loss grows with the square of the distance from target, not just when a limit is crossed. The loss for one unit is k times the deviation squared. #### How do I estimate A0? **Answer:** Take the average cost incurred when a unit is at the limit: scrap or rework cost, plus handling, plus an estimate of field failure or customer disruption cost. Ask finance for the figures and show a low and a high case. #### Does this replace Cpk? **Answer:** No. Cpk measures capability against a limit, while the loss function measures cost of deviation from target. They complement each other: a high Cpk can still carry meaningful loss if the process is not on target. #### What about one-sided characteristics? **Answer:** Smaller-is-better uses L = k y^2 and larger-is-better uses L = k / y^2. This calculator covers the nominal-is-best case only. ## Search terms taguchi loss function calculator, quadratic loss function example, cost of variation calculator, taguchi loss k constant, nominal is best loss function, quality loss function formula, cost of poor centering --- Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json