Modified Data Envelopment Analysis of Multiple Response Experiments in the Robust Parameter Design Procedures

Selecting the optimum process parameter level setting for multi-quality processes is cumbersome. Robust parameter designs procedure that utilizes different strategies for improving performance/productivity during product and process design so that quality response can be obtained efficiently and optimally. An inevitable problem that is associated with the product and process design is in appropriating process variables that will yield optimal response. The complexity of the problem is peculiar with multiple response experiments (processes) where different factor level combinations yield varying responses. Previous methods are plagued with complex computational search, unrealistic assumptions, ignoring the interrelationship between responses and failure to select optimum process parameter level setting. This thesis proposes the implementation of modified variable return to scale (VRS) data envelopment analysis in the Robust Parameter Design (RPD) procedures to estimate and optimize responses of all non-dominated (significant) factors level combinations in multi-response experiments. This study also enhances the discriminatory tendency of the model by imposing VRS partitioning within the model. The model is conducted in a manner that with an adequate BPNN topology, experiment with incomplete, missing or censored data whenever encountered, could be investigated. Here, standard DEA modes are allowed to self-assess, the upper bound is restricted and the VRS penalization coefficient is adopted to determine the optimum process parameter level setting. The proposed procedures are applied to seven different case studies and the results were compared with existing methods of principal component analysis (PCA), DEA based ranking approach (DEAR), genetic algorithm (GA), grey relational analysis (GRA) and benevolent formulation (BF). The effectiveness of the proposed model measured by the total anticipated improvement yielded the highest total improvement over the existing methods. In overall, many inefficient DMUs that would have been promoted as efficient by the standard DEA models were revealed. The discriminative tendency further gives insight to DMUs that are within the convex set of the factor level settings and those that are not, thereby making the computation search for the optimal easy and simple.