Loss Functions - Loss functions relate monetary cost or penalty to variation from a Target. The form of the relationship is usually chosen as linear, quadratic or inverted Gaussian. The user must provide the Target and the cost or penalty at key values of the response deviating from the target.
Alternatively, a common mis-perception is that the specifications, or requirements, are like goal posts: so long as you deliver within the goal posts, you are doing well. There is equal value for all products or services within the goal posts (zero value beyond the specifications), so there is no advantage in improvement beyond this point.
Loss functions recognize the fallacy of the goal post approach. There is not equal value within the specifications, and customer satisfaction is not maximized at any point between the specifications. Instead, customers tend to think in terms of optimums. The optimal value for the product or service is at the midpoint of the requirements, and deviations from that point are less desirable. The customer instead values predictability, or minimum variation, so that their processes are impacted to a minimal degree.
Learn more about the Regression tools in Six Sigma Demystified (2011, McGraw-Hill) by Paul Keller, in his online Regression short course (only $99), or his online Black Belt certification training course ($875).