Probabilistic tolerance design for a subsystem under burr distribution using taguchi's loss functions

Abstract

Taguchi (1986) has derived tolerances for subcomponents, subsystems, parts and materials in which the relationship between a higher-level (Y) and a lower-level (X) quality characteristic is assumed to be deterministic and linear, namely, Y=α+βX, without an error term. Tsai (1990) developed a probabilistic tolerance design for a subsystem in which a bivariate normal distribution between the above two quality characteristics as well as Taguchi's quadratic loss function were considered together to develop a closed form solution of the tolerance design for a subsystem. The Burr family is very rich for fitting sample data, and has positive domain. A bivariate Burr distribution can describe a nonlinear relationship between two quality characteristics, hence, it is adopted instead of a bivariate normal distribution and the simple solutions of three probabilistic tolerance desings for a subsystem are obtained for three cases of “nominal-is-best”, “smaller-is-berrer”, and “larger-is-beter” quality characteristics,...