Applications of the upside-down normal loss function

Abstract

The upside-down normal loss function (UDNLF) is a weighted loss function that has accurately modeled losses in a product engineering context. The function's scale parameter can be adjusted to account for the actual percentage of material failing to work at specification limits. Use of the function along with process history allows the prediction of expected loss-the average loss one would expect over a long period of stable process operation. Theory has been developed for the multivariate loss function (MUDNLF), which can be applied to optimize a process with many parameters-a situation in which engineering intuition is often ineffective. Computational formulae are presented for expected loss given normally distributed process parameters (correlated or uncorrelated), both in the univariate and multivariate cases.

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