The Taguchi loss function implies that there is some loss associated with any deviation from the target. This loss will be negligible when the output is close to the target, but it may be quite considerable as we approach the specification limits.

We know that the output of the process will be distributed about the process average, so that each item will have a greater or lesser associated loss. It is possible, then, to calculate the expected average loss per unit for the process. In order to do this, we need to know two things:

• the average variation in the output
  
  
• how far the process average is from the target

The equation to calculate the average loss uses the values of sigma(X) and (the process average) to provide this information.

The average loss will increase as the process average moves farther away from the target, or the variance of the output (sigma(X)²) increases. Therefore, the average loss will be lowest when the process is operating on target, and the variation is minimal.

Some people advocate the use of relaxed control limits when the process capability is high. This is because the process average can shift by some large degree without producing any non-conforming output. The idea of relaxed limits is that they reduce the amount of time spent tracking down assignable causes which do not affect the ability of the process to meet the specifications. We hope that the discussion of the Taguchi loss function has shown that this is a false economy. The quality of the process output will be highest, and the associated loss (both directly to the manufacturer, and to the customer) will be lowest, when:

• the process is in control so that the variation is minimal
  
  
• the process is operating as close to the target as possible