An application of Fuzzy signal-to-noise ratio to the assessment of manufacturing processes

Abstract

Taguchi method is an important tool used for robust design to produce high quality products efficiently. In Taguchi method, the signal-to-noise (SN) ratio serves as the objective function for optimization. This ratio is a useful measurement indicator for manufacturing processes. Conventionally, one calculates the SN ratio with the crisp observations. However, there are cases that observations are difficult to measure precisely, or observations need to be estimated. This paper develops a fuzzy nonlinear programming model, based on the SN ratio, to assess the manufacturing processes with fuzzy observations. A pair of nonlinear fractional programs is formulated to calculate the lower and upper bounds of the fuzzy SN ratio. By model reduction and variable substitutions, the nonlinear fractional programs are transformed into quadratic programs. Solving the transformed quadratic programs, we obtain the global optimum solutions of the lower bound and upper bound fuzzy SN ratio. By deriving the ranking index of the fuzzy SN ratios of the manufacturing process alternatives, the ranking result of the assessment is determined.