Conference article

An efficient and easy discretizing method for the treatment of noise factors in Robust Design

Antonio Lanzotti
Department of Aerospace Engineering, University of Naples "Federico II", Italy

Amalia Vanacore
Department of Aerospace Engineering, University of Naples "Federico II", Italy

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Published in: 10th QMOD Conference. Quality Management and Organiqatinal Development. Our Dreams of Excellence; 18-20 June; 2007 in Helsingborg; Sweden

Linköping Electronic Conference Proceedings 26:102, p.

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Published: 2008-02-15


ISSN: 1650-3686 (print), 1650-3740 (online)


A critical issue for Robust Design practitioners is to take in due consideration the continuous nature of some noise factors and face; consequently; the problem of choosing and properly weighting a few representative levels for these factors to use for experiments.

Taguchi (1978) proposed a simple way to discretize a continuous distribution pointing out the relevance of the problem. D’Errico and Zaino (1988) improved the previous technique and generalised Taguchi results. After these works; several discretization techniques have been proposed in literature (Seo & Kwak; 2002). Besides the extensions of the three-level Taguchi method; the most common approaches are numerical quadrature; matching moments; Monte Carlo simulation. However most of these methods fails to strike a balance between accuracy and computational complexity.

In this work; an efficient and easy statistical method to find an equivalent discrete distribution for a continuous random variable (r.v.) is proposed. The proposed method is illustrated by applying it to the treatment of the anthropometrical noise factors in the context of Robust Ergonomic Design (RED; Lanzotti 2006; Barone S. and Lanzotti A.; 2007).

In general; the anthropometrical noise factor can be modelled by a univariate/multivariate continuous variable (e.g. the stature or/and the weight of a class of users); or a mixture of univariate/multivariate continuous variables (e.g. the stature or/and the weight of two or more classes of users). In these cases an efficient way to approximate the anthropometrical continuous noise factors by a finite number of experimental levels is needed.

The article has the following structure: in Section 2; two traditional techniques commonly used in statistical tolerancing (Taguchi; 1983; D’Errico and Zaino; 1988) together with a method recently introduced for the treatment of the anthropometrical noise factor in RED (Lanzotti A.; 2006; Barone S. and Lanzotti A.; 2007) are briefly illustrated and reviewed. In Section 3; starting from the main criticisms of the reviewed methods; a new discretizing technique is proposed. In Section 4; the method is applied and compared with previous ones for univariate and mixture of Normal random variables (r.v.s). Section 5 provides final comments and conclusions.


Discrete Approximation; Noise Factor; Robust Ergonomic Design; Taguchi’s Method


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