Spiring, Fred (1991, ASQC) The University of Manitoba, Winnipeg, Manitoba, CANADA
This abstract is an edited version of the author's original.
The squared error loss function has been used by statisticians and economists to examine the quality of estimators; Taguchi used a squared error loss function to demonstrate the need to consider proximity to the target while assessing quality. This paper proposes a new loss function that addresses some of the shortcomings of the traditional square error loss function and examines its properties of the new loss function.
Quality assurance practitioners and researchers have criticized the squared error loss function for: (1) failure to provide a quantifiable maximum loss, (2) the magnitude of losses associated with extreme deviations from the nominal, and (3) the inability to consider asymmetric losses.
The traditional squared error loss function is decreasing in the interval (-�T] and increasing for [T, �where T denotes the target or nominal and must be modified in order to incorporate a maximum loss. Taguchi addressed this problem by first finding the tolerance limits where the quality loss is equal to the cost of manufacturing and then examining the points where the squared error loss function intersects the maximum loss. The result is a piecewise loss function.An alternative loss function is proposed that allows a single function (in the symmetric case) to describe the loss. The proposed loss function is simply a mirror image of the standard Gaussian curve. The curve is smooth, has a minimum at the nominal and quantifiable maximum, and it satisfies the usual demands required of a squared error loss function.
Quality assurance (QA),Quality improvement (QI),Loss functions,Statistics,Taguchi method,Gaussian curve