The latter has been widely adapted to the tolerance

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Unformatted text preview: ion problem (3) will indeed result in a minimized production cost for the manufacturer. 2.3. Quality loss Taking into account the quality loss the assembled variation brings to the customer, it is favorable to add a penalty function y a L( y ) to the objective function. The penalty function punishes a deviation from target (T) for each measure. 118 J. Lööf, T. Hermansson and R. Söderberg Taguchi used a quadratic penalty function (4) [Taguchi et al., 1989]. L( y ) = z ( y − T ) 2 (4) Choi used the quadratic loss function (4) for the tolerance allocation problem [Choi et al., 2000]. Söderberg refined this approach further by introducing the monotonic loss function [Söderberg, 1995]. The asymmetric quadratic loss function (5) punishes the deviation from the target differently depending on the direction. L( y ) = z1 ( y − T ) 2 z2 ( y − T ) 2 y<T y≥T (5) Since a loss function on this form has the (stochastic) variable y as input, whereas our optimization problem (3) is stated in the tolerances ti, the expectance of L constitutes a good measure on the quality loss in terms of (3): E [ L( y ) ] = ∫ ∞ −∞ L( y ) F ( y )dy , (6) where F(y) is the probability density fun...
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This note was uploaded on 08/03/2010 for the course DD 1234 taught by Professor Zczxc during the Spring '10 term at Magnolia Bible.

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