Taguchi (1978) proposed a simple way to discretize a continuous distribution pointing out the relevance of the problem. Dâ€™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; Dâ€™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.
Keywords: Discrete Approximation; Noise Factor; Robust Ergonomic Design; Taguchiâ€™s Method