We present an analysis of the previously proposed “modified quadratic” loss function. This loss model integrates elements from both Classical Taguchi and Goal Post manufacturing loss models. Specifically, the analyzed hybrid model follows the Taguchi loss quadratic dependence between the upper and lower manufacturing specification limits. On the other hand, outside of these limits, the loss rule is in agreement with the Goal Post Model. Supported by the results of analysis contained herein the Taguchi-Hybrid model does not overestimate the loss as is inherent to the classical Taguchi model. Also, the proposed Taguchi Hybrid model does not ignore deviations from the exact target and hence will not under-estimate the manufacturing loss a symptom characteristic of the Goal Post Model.

The analysis for the Taguchi-Hybrid is employed on assuming two different distributions describing the manufacturing parameters namely uniform and Gaussian distributions. The exact analysis is provided for these part distributions including the possibility the mean is both on and off of the ideal target value, i.e. with and without target bias. For the assumption of Gaussian part distribution, the expectation of the Taguchi Hybrid loss function is representable in terms of process capability and normalized target bias. It is observed in the Gaussian PDF case the expectation of the Hybrid Taguchi loss function can be cast into a five-term representation. In this representation two of the terms are the classical Taguchi loss and the Goal Post loss and the remaining three are “negative” corrective losses. These remaining three serve to compensate for overestimation of loss from the first two terms. A wide range of tests was performed with the analytical model for assumptions of parts being distributed both Uniform and Gaussian. Numerical integration was employed to validate the derived dependencies for the associated loss expectations.

A hypothetical example for voltage regulator drift demonstrates that in the Uniform distribution case the predicted loss of the Hybrid Taguchi model lies between loss predictions generated from the more conservative Taguchi Loss and least conservative Goal Post Loss models. A second hypothetical example details a procedure to generate salient target bias design limits for the metal oxide semiconductor field effect (MOSFET) transistor channel length. In this procedure considerations were applied to both the expectation for Taguchi-Hybrid Goal Post loss dependence and similarly for Taguchi-Hybrid Quadratic losses. With reasonable loss limits assigned for these expectations it was found that the process design rule for target bias was being controlled by the limit imposed on the Taguchi-Hybrid Quadratic loss which is related to quality of parts passing inspection and not the fraction of parts rejected.

Date of publication

Summer 7-31-2019

Document Type




Persistent identifier


Committee members

Ron Pieper, Mukul V. Shirvaikar, Premananda Indic



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