A general loss function based optimization procedure for robust design

The concept of quality loss introduced by Taguchi is employed in the synthesis of designs that are insensitive to variations in controllable variables and uncontrollable parameters. A new design approach that achieves robustness by minimizing the expected value of a loss function based on a design’s performance characteristic, and which is applicable to a general design situation, is proposed. The design constraints are stated in terms of their expected values. Both design variables and parameters are assumed to fluctuate about their nominal values. To ensure that in the pursuit of robustness, product performance is not compromised, the procedure constraints the expected value of the performance characteristic at its target value. Constraint violations that might be caused by fluctuations in design variables, or parameters, or both, are handled by reducing the feasible design space with the addition of a constraint sensitivity term, obtained using a linear statistical analysis. Two scenarios- one of which is applicable when the tolerances of the design variables are fixed, and the other to situations where the tolerances are treated as unknowns, are considered. The mechanics of this approach is illustrated by solving two examples. The first example involves the determination of the shape and configuration variables of a two bar truss; which is to be designed for minimum weight while being subject to stress constraints. The second example is a minimum cost welded beam design problem; where the dimensions of the weldment and the beam are found without exceeding the limitations stated on the shear stress in the weld, normal stress in the beam, buckling load on the beam and tip deflection of the beam. The utility of the robust design method and the reasons for its choice over a conventional design procedure are discussed. The methodology presented in this work is expected to be useful in designing robustness in machines, structures and other products where the system can be modelled using algebraic equations.