The reflected normal loss function

The use of loss functions in quality assurance has grown steadily with the introduction of Taguchi's philosophy. The quadratic loss function has been used by decision‐theoretic statisticians and economists for many years. Taguchi uses a modified form of the quadratic loss function to demonstrate the need to consider proximity to the target while assessing quality. Several authors have suggested that the traditional quadratic loss function is inadequate for assessing quality and quality improvement. A new, easily understood loss function, based on a reflection of the normal density function, is presented, and some associated statistical properties discussed.