A comparative study on optimization methods for experiments with ordered categorical data

When conducting experiments, the selected quality characteristic should as far as possible be a continuous variable and be easy to measure. Due to the inherent nature of the quality characteristic or the convenience of the measurement technique and cost-effectiveness, the data observed in many experiments are ordered categorical. To analyze ordered categorical data for optimizing factor settings, there are three widely accepted approaches: Taguchi’s accumulation analysis, Nair’s scoring scheme and Jeng’s weighted probability scoring scheme. In this paper, a simpler method named the weighted SN ratio method for analyzing ordered categorical data is introduced. A case study involving optimizing the polysilicon deposition process for minimizing surface defects and achieving the target thickness in a very large-scale integrated circuit can demonstrate the four approaches. Finally, comparative analyses of efficiency for employing the four approaches to optimize factor settings are presented according to simulated experimental data that are normally, Weibull and Gamma distributed. From the results, it is obvious that the weighted SN ratio method has the properties of easy computation and uses one-step optimization to obtain the optimal factor settings. Its efficiency is slightly less than that of the scoring scheme, better than that of the accumulation analysis and the weighted probability-scoring scheme.