| A methodology is provided and demonstrated for robust design of the batch dyeing process. The robust design problem is defined in terms of design objectives, control factors and noise factors. Objective quantitative measures are developed to evaluate mean and dispersion characteristics of dyeing performance in terms of color match to a standard, color uniformity and color repeatability. Design of experiments is discussed for developing empirical models of the performance measures. Experiments are designed and performed in a dye laboratory for the case problem. A methodology is presented for analyzing data from the designed experiments, and it is demonstrated using the data collected. Empirical models of the performance measures are developed for the case problem. Then, using the empirical models, the robust design problem is formulated as a multi-objective nonlinear programming (NLP) problem. Alternative formulations are discussed. The NLP problem is solved to obtain best settings of controllable process parameters for the study case. Selected parameter settings are tested in the laboratory. The experimental results are compared with the model predictions. Effects of experimental errors, model assumptions, and the experimental design and modeling approach on the results are discussed. For unconfirmed results the iterative use of the robust design methodology is described. A heuristic approach, the use of adjustment parameters, is also presented. |
