Taguchi´s Loss Function

Definition

Simply put, the Taguchi loss function is a way to show how each non-perfect part produced, results in a loss for the company. Deming states that it shows

"a minimal loss at the nominal value, and an ever-increasing loss with departure either way from the nominal value." - W. Edwards Deming Out of the Crisis. p.141

A technical definition is

A parabolic representation that estimates the quality loss, expressed monetarily, that results when quality characteristics deviate from the target values. The cost of this deviation increases quadratically as the characteristic moves farther from the target value. - Ducan, William Total Quality Key Terms. p. 171

Graphically, the loss function is represented as shown above.

Interpreting the chart

This standard representation of the loss function demonstrates a few of the key attributes of loss. For example, the target value and the bottom of the parabolic function intersect, implying that as parts are produced at the nominal value, little or no loss occurs. Also, the curve flattens as it approaches and departs from the target value. (This shows that as products approach the nominal value, the loss incurred is less than when it departs from the target.) Any departure from the nominal value results in a loss!

Loss can be measured per part. Measuring loss encourages a focus on achieving less variation. As we understand how even a little variation from the nominal results in a loss, the tendency would be to try and keep product and process as close to the nominal value as possible. This is what is so beneficial about the Taguchi loss. It always keeps our focus on the need to continually improve.

A business that misuses what it has will continue to misuse what it can get. The point is--cure the misuse. - Ford and Crowther

Application

A company that manufactures parts that require a large amount of machining grew tired of the high costs of tooling. To avoid premature replacement of these expensive tools, the manager suggested that operators set the machine to run at the high-end of the specification limits. As the tool would wear down, the products would end up measuring on the low-end of the specification limits. So, the machine would start by producing parts on the high-end and after a period of time, the machine would produce parts that fell just inside of the specs.

The variation of parts produced on this machine was much greater than it should be, since the strategy was to use the entire spec width allowed rather than produce the highest quality part possible. Products may fall within spec, but will not produce close to the nominal. Several of these "good parts" may not assemble well, may require recall, or may come back under warranty. The Taguchi loss would be very high.

We should consider these vital questions:

* Is the savings of tool life

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