Bounded loss functions and the characteristic function inversion method for computing expected loss

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6 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)401-421
Journal / PublicationQuality Technology and Quantitative Management
Volume11
Issue number4
Publication statusPublished - 2014
Externally publishedYes

Abstract

In robust parameter design, the quadratic loss function is commonly used. However, this loss function is not always realistic and the expected loss may not exist in some cases. This paper proposes the use of a general class of bounded loss functions that are cumulative distribution functions and probability density functions. New loss functions are investigated and the loss functions are shown to yield optimal settings different from those obtained with the quadratic loss. For the class of models that are linear in the noise factors, we give a numerical method based on characteristic function inversion for computing expected loss. The method is quick and accurate; thus, it eases computation of the expected loss and comparison of alternative control factor settings. This method is applicable as long as the distributions chosen to represent the loss function and noise factors have tractable characteristic functions.

Research Area(s)

  • Bounded loss functions, Numerical inversion of characteristic functions, Robust parameter design