The Robust Design of Static and Dynamic Systems Using the Stochastic Frontier Method

Dr. G. Taguchi first established the robust design technique, which tries to regulate a system’s input variables so that the functional performance or system response is insensitive to numerous environmental and degradation sources of variation. Moreover, when the noise factors behave in an anti-synergistic and non-monotonic way, non-optimal design parameters may amplify the system variance. In turn, this causes the performance characteristic to deteriorate and stimulates the initiation of special-cause variability. To optimize superior design of products/processes against noise sources, the paper proposes a novel robust design method, which uses designed experiments and the stochastic frontier (SF) method-ology. The math model of the stochastic frontier method is rooted in decomposing the error term (system residual variation) into a neoclassic normal error term ( \(\left( {{\text{V}}_{i} \mathop {iid}\limits_{ \sim } {\text{N}}\left( {0,\sigma _{v}^{2} } \right)} \right)\) ) and a semi-normal error term ( \(\left( {U_{i} \mathop {iid}\limits_{ \sim } \left| {N\left( {\mu ,\sigma _{u}^{2} } \right)} \right|} \right)\) ). The virtue of the proposed method is finally demonstrated using an industrial case study.