In this section the basic mathematical formulation of Taguchi’s loss function is developed, and an outline of the steps used to apply the loss function is presented. The loss function has proven to be an excellent tool for determining the magnitude of the process (manufacturer) and supplier tolerances, based on quality as perceived by the customer. The methodology for realignment of tolerances is beyond the scope of this text. Taguchi defined the loss function as deviation as a quantity proportional to the deviation from the target quality characteristic. At zero deviation, the performance is on target and the loss is zero. An organization seriously committed to achieving higher standards of quality in an optimum manner may develop families of loss curves for each process. The loss function concept has two practical applications. The primary application is for estimating the potential cost savings resulting from the improvements achieved by optimizing a product or process design. The loss function can serve as a measure of performance regardless of the method of the quality improvement. As long as variation is reduced by corrective actions or design improvements, the loss function presents a means for estimating the savings in terms of dollars and cents. It can also be used to determine if an investment to reduce variation is worth the cost. The second application is to determine manufacturer and supplier tolerances based on the customer’s perception of the quality range. In this case, the loss function provides an objective way to set the limits for the inspection of products at the manufacturer or supplier location. When improvement is achieved, it is necessarily reflected in lowering the standard deviation (variance) and/or reducing the distance of mean performance from the target. Of course, when variation is reduced, with or without change in distance to the target, common performance measures like capability indices (Cp and Cpk) increase and Taguchi loss (L) decreases. While all of these numerical indices are easily computed, for better visualization of the improvement a plot of the distribution is most desirable.