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Most of the studies of quality systems or product assessment deal with a single quality characteristic to determine the quality loss. From the customer's point of view, however, products are often judged by more than one quality characteristic. For this reason, a multivariate quality loss function is required as an extension to the Taguchi loss function to capture the overall losses caused by bad quality when multiple quality characteristics are present. A numerical example is illustrated showing that using inappropriate univariate loss functions will give an underestimated quality loss or even ignored the loss incurred because of the poor quality.

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Most of the studies of quality system or productquality assessment deal with a single quality characteristic to determine the quality loss. Products are often assessed on more than one quality characteristic. For this reason, different multivariate quality loss functions have been proposed. However, these loss functions only consider the nominal-the-best quality characteristics (N-type); they do not consider the condition when the quality characteristics are of the smaller-the-better (S-type).In this article, we present a quality evaluation model using loss function for multiple S-type quality characteristics. A numerical example is illustrated showing that using inappropriate loss functions will lead to inaccurate results that give either an underestimate or overestimate of the expected quality costs.