G. Taguchi pointed out that both the manufacturer's and society's expected loss (or cost) is reduced when the results of a process are centered on the intended target value with little variation. The loss (cost) is ever increasing as those same product characteristics depart from their targets. The expected loss also depends on where the distribution is, relative to the target. The Taguchi loss function is often shown as a parabolic curve, but in some situations the loss function is asymmetric with respect to the target, or desired value.
The Taguchi Loss Function is a graphical depiction of loss developed by the Japanese business statistician Genichi Taguchi to describe a phenomenon affecting the value of products produced by a company. Quality does not suddenly plummet when, for instance, a machinist exceeds a rigid blueprint tolerance. Instead "loss" in value progressively increases as variation increases from the intended condition. This was considered a breakthrough in describing quality, and helped fuel the continuous improvement movement that since has become known as lean manufacturing.
The Taguchi Loss Function is important for a number of reasons. Primarily, to help engineers better understand the importance of designing for variation. It was important to the Six Sigma movement by driving an improved understanding of the importance of Variation Management. Finally, It was important to describing the effects of changing variation on a system, which is a central characteristic of Lean Dynamics, a business management discipline focused on better understanding the impact of dynamic business conditions on loss, and thus on creating value.