Lean Manufacturing and Six Sigma Definitions

Glossary terms, history, people and definitions about Lean and Six Sigma

Taguchi Loss Function

Developed by Genichi Taguchi, it is a graphical representation of how an increase in variation within specification limits leads to an exponential increase in customer dissatisfaction.

The common thinking around specification limits is that the customer is satisfied as long as the variation stays within the specification limits (Figure 5). If the variation exceeds the limits, then the customer immediately feels dissatisfied. The specification limits divide satisfaction from dissatisfaction. For example, if the lower limit is 10, and the upper limit is 20, then a measurement of 19.9 will lead to customer satisfaction, while a measurement of 20.1 will lead to customer dissatisfaction.

However, Taguchi states that any variation away from the nominal (target) performance will begin to incur customer dissatisfaction. As the variation increases, the customer will gradually (exponentially) become dissatisfied. In the previous example, if the measurement is 19.9, the customer will be dissatisfied more than a measurement of 19.8. If the measurement is 20.1, the customer will be slightly more dissatisfied than the measurement of 19.9.

Taguchi states that the specification limits do not cleanly separate satisfaction levels for the customer. Any variation away from the nominal (value of 15 in the example above) will start to incur customer dissatisfaction. The quality does not suddenly plummet once the limits are exceeded, rather it is a gradual degradation as the measurements get closer to the limits. The goal of a company should be to achieve the target performance with minimal variation. That will minimize the customer dissatisfaction.

A real life example of the Taguchi Loss Function would be the quality of food compared to expiration dates.

If you purchase an orange at the supermarket, there is a certain date that is ideal to eat it. That would be the target date. There will also be limits for when to eat the orange (within three days of the target date, Day 2 to Day 8).

days until orange fruit ripeness

For this example, Day 5 represents the target date to eat the orange. That is when the orange will taste the best (customer satisfaction).

You purchase the orange on Day 1, but if you eat the orange you will be very dissatisfied, as it is not ready to eat. This would fall below the lower limit. On Day 3 it would be acceptable to eat, but you are still dissatisfied because it doesn’t taste as good as eating on the target date. If you wait for Day 5, you will be satisfied, because it is eaten on the ideal date. If you wait until Day 7, you will be slightly dissatisfied, because it is one day past the ideal date, but it will still be within the limits provided by the supermarket. If you wait until Day 9, you will be very dissatisfied, as it will be too far past the ideal date.

taguchi loss function limits dissatisfaction

You are slightly dissatisfied from Day 2 through 4, and from Day 6 through 8, even though technically you are within the limits provided by the supermarket. The least amount of dissatisfaction occurs on the target date, and each day removed from the target date incurs slightly more dissatisfaction. Contrary to most discussions around specification limits, you are NOT completely satisfied from Days 2 through 8, and only dissatisfied on Day 1 and 9.

animation from The Red Road showing reduction in loss as variation decreases

A real-life example in the video below was documented back in the 1980’s when Ford compared two transmissions from different suppliers. The supplier with less variation also had less warranty claims, even though both suppliers met the specifications (blueprints).

For more practical examples of this theory, consider the following real life examples, where hitting a target is ideal, and getting too far away from the target would incur problems.

  • Ripened fruit
  • Pool water temperature
  • Shoe size
  • Viewing location for a solar eclipse
  • Parking alignment within parking spot