Results in statistical process design and improvement
Date of Completion
Engineering, Electronics and Electrical|Engineering, Industrial|Operations Research
This dissertation contributes extensions to the methodology of experimental design and optimization of product designs and manufacturing processes toward making it a more comprehensive and universally applicable technique for quality improvement. It does so by pursuing three objectives: bringing the design problem in the purview of multiobjective optimization; offering an approach to handle model uncertainty in optimization problems; and exploring a method for experiment selection for on-line improvement of processes.^ The simultaneous optimization of several conflicting quality metrics pertaining to a product/process with respect to design parameters is formulated as a vector optimization problem. The approach reduces the design process to the achievement of a solution in a set called the set of nondominated or Pareto-optimal solutions. Two methods, goal programming and the method of reference points, are applied to the design-for-quality problem of obtaining a compromise design closest to the decision-maker's preferences. The cases of discrete and continuous parameters are considered separately. In the continuous parameter case, the consequence of using regression models to obtain the objective functions is examined. The uncertainty in the multiobjective optimum obtained using these models is evaluated via Monte Carlo simulations--an idea heretofore unexplored for evaluating the statistics of optima obtained from uncertain cost functions. This approach is found to account for model uncertainty more reliably than some existing methods. In the discrete parameter case, an efficient two-step search method is presented to identify the set of nondominated solutions for the case of linear models.^ Towards solving: the problem of experiment selection for on-line improvement, the use of two-level fractional-factorial experiments is proposed as a means for rapid ascent to the optimum, while minimizing the number of unacceptable products resulting from undesirable perturbations. The reliability of inferences from fractional-factorial experiments is improved by developing a method for placing the design points to minimize the effect of worst-case, unaccounted-for interactions. ^
Mathur, Amit, "Results in statistical process design and improvement" (1996). Doctoral Dissertations. AAI9707203.