Fuzzy nonlinear programming approach to the evaluation of manufacturing processes

The quality of a product produced by a manufacturing process should be able to lie within an acceptable variability around its target value. The signal-to-noise (S/N) ratio, served as the objective function for optimization in Taguchi methods, is a useful tool for the evaluation of manufacturing processes. Most studies and applications focus on the calculation of S/N ratios with deterministic observations, and the literature receives little attention to the consideration of S/N ratio with fuzzy observations. This paper develops a fuzzy nonlinear programming model to calculate the fuzzy S/N ratio for the assessment of the manufacturing processes with fuzzy observations. A pair of nonlinear fractional programs is formulated to calculate the lower and upper bounds of the fuzzy S/N ratio. By model reduction and variable substitutions, this pair of nonlinear fractional programs is transformed into quadratic programs. Solving the transformed quadratic programs, we obtain the optimum solutions of the lower bound and upper bound fuzzy S/N ratio. By deriving the ranking indices of the fuzzy S/N ratios of manufacturing process alternatives, the evaluation result of the alternatives is obtained.