In the manufacturing processes, process optimization tasks, to optimize their product quality, can be performed through the following procedures. First, process models mimicking functional relationships between quality characteristics and controllable factors are constructed. Next, based on these models, objective functions formulating process optimization problems are defined. Finally, optimization algorithms are applied for finding solutions for these functions. It is important to note that different solutions can be found whenever these algorithms are independently executed if a unique solution does not exist; this may cause confusion for process operators and engineers. This paper proposes a confidence interval (CI)-based process optimization method using second-order polynomial regression analysis. This method evaluates the quality of the different solutions in terms of the lengths of their CIs; these CIs enclose the outputs of the regression models for these solutions. As the CIs become narrower, the uncertainty about the solutions decreases (i.e., they become statistically significant). In the proposed method, after sorting the different solutions in ascending order, according to the lengths, the first few solutions are selected and recommended for the users. To verify the performance, the method is applied to a process dataset, gathered from a ball mill, used to grind ceramic powders and mix these powders with solvents and some additives. Simulation results show that this method can provide good solutions from a statistical perspective; among the provided solutions, the users are able to flexibly choose and use proper solutions fulfilling key requirements for target processes.

The characteristics of an internal slurry were analyzed during ball milling, which is commonly utilized in ceramic processing. We used a device with a capacity of 50 L because this is the size employed in industries and built a circulation system to collect the slurry during milling. The slurry was characterized in terms of the particle size and viscosity, and vibration data were collected from the side of the ball mill drum in real time for 24 h. By applying a fast Fourier transform to the vibration data, the energy was calculated and compared with the slurry characteristics. The vibration data in the (3–4) kHz range showed a strong negative correlation with the slurry viscosity at a shear rate of 24s⁻¹. Our results confirm that the characteristics of the internal slurry can be monitored in real time using the vibration data collected during ball milling. Graphical abstract