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Quadratic Quality Loss Functions and Signal-to-Noise Ratios for a Trivariate Response

机译：三元响应的二次质量损失函数和信噪比

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摘要

This paper extends Taguchi's quadratic quality loss function (QQLF) and signal-to-noise (S/N) ratios to a trivariate case by considering correlations between all pairs of quality characteristics. Single static quality characteristics (QCHs) are classified as: (1) smaller the better (STB), (2) larger the better (LTB), and (3) nominal the best (NTB). Initially, Taguchi studied single-response models. Later Chang (1993), Maghsoodloo and Chang (2001), and Maghsoodloo and Huang (2001) obtained relationships for the bivariate response cases. Chang (1993) and Maghsoodloo and Chang (2001) developed relationships for cost coefficients of the bivariate QQLF and S/N ratios for the cases of (NTB, NTB), (STB, STB), and (LTB, LTB). Later Maghsoodloo and Huang (2001) developed relationships for the remaining cases, which are (STB, LTB), (STB, NTB), and (LTB, NTB). This paper extends the number of variates from two to three, which are correlated, and obtains relationships between cost coefficients to ensure that the cost matrix is positive definite (pd). Also, S/N ratios are developed for all combinations of trivariate responses.
机译：本文通过考虑所有质量特性对之间的相关性，将田口的二次质量损失函数（QQLF）和信噪比（S / N）比扩展到三变量情况。单一静态质量特征（QCH）分为：（1）越小（STB）越好；（2）越大（LTB）越好；（3）标称最佳（NTB）。最初，Taguchi研究了单响应模型。后来，Chang（1993），Maghsoodloo和Chang（2001）以及Maghsoodloo和Huang（2001）获得了双变量反应病例的关系。 Chang（1993）和Maghsoodloo和Chang（2001）为（NTB，NTB），（STB，STB）和（LTB，LTB）的情况开发了二元QQLF和S / N比的成本系数之间的关系。后来，Maghsoodloo和Huang（2001）为其余案例建立了关系，分别是（STB，LTB），（STB，NTB）和（LTB，NTB）。本文将变量的数量从2个扩展为3个，并将它们相关，并获得成本系数之间的关系，以确保成本矩阵为正定（pd）。同样，针对三变量响应的所有组合开发了信噪比。

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