Product design is increasingly complicated and some quality characteristics cannot be directly measured. These quality characteristics are generally classified into several categories by visually examining the externals of products and forming an ordered system response. Most studies of quality improvement focus primarily on the quantitative form. Studies of ordered categorical response in a state system have been proposed over recent years. However, cases of an ordered categorical response in a dynamic system have rarely been seen. This study utilises grey relational analysis, from grey system theory, to develop a procedure for improving the ordered categorical response in a dynamic system, based on Taguchis parameter design. The proposed procedure can determine effectively the optimal factor level combination for an ordered categorical response in a dynamic system. A case study for improving the uniformity of plating in the lead frame process involved in semiconductor packaging is provided to demonstrate the effectiveness of the proposed procedure.