No abstract

This research developed mathematical models to optimize process performance for multiple pentagon fuzzy quality responses. Initially, each quality response was represented by a pentagon membership function. Then, the combination of optimal factor levels was obtained for each response replicate. Those optimal combinations were then used to construct pentagon regression models for each response. A pentagon fuzzy optimization model was formulated and solved to determine the combination of optimal factor levels at each element of pentagon response's fuzzy number. Two real case studies, i.e. wireelectrical discharge machining and sputtering process, were provided for illustration. Optimal results of the two case studies revealed that the proposed procedure effectively optimized performance under uncertainty and provided larger improvement in multiple quality characteristics. In conclusion, the proposed procedure may enhance the process engineer's knowledge about effects of uncertainty on process/product performance and help practitioners decide the proper adjustments of factor levels in order to enhance performance of electrical discharge machining and sputtering process.

This research proposed a procedure that combines genetic algorithm (GA) technique and fuzzy goal programming to optimize process performance in experimental design for fuzzy multiple quality characteristics. Initially, regression models were formulated to relate each replicate of a quality characteristic with the process's controllable factors. The GA technique was then employed to determine the optimal factor settings for each response's replicate. The GA's optimal results were then deployed to develop a fuzzy regression model to relate fuzzy process settings with each quality characteristic. The fuzzy models were adopted to construct the fuzzy desirability and deviation matrices for all quality characteristics. Finally, three optimization models were developed to determine the lower, middle, and upper bounds of optimal factor settings. Three industrial applications, which were widely examined, were employed to illustrate the proposed procedure. Results revealed that the proposed GA-fuzzy procedure efficiently dealt with uncertainty in multiple quality characteristics and process settings by providing fuzzy optimal factor settings rather than crisp values. Such information can support process engineering in understanding the impact of variations/uncertainty on process and product performance and in deciding proper corrective and preventive actions. Compared to the Taguchi method, grey-Taguchi technique, and artificial neural networks approach, the proposed procedure is found efficient in optimizing process performance for multiple quality characteristics under uncertainty.