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Taguchi Method is not limited only quality design but extended to many application fields in the using. However, it does not yet study on a multi characteristic design method that has many characteristics although it concentrates upon a parameter design method that has only one characteristic of product. Actually, if quality of product is managed, multi characteristic of product is largely concerned at the same time. There are also many cases that multi characteristic problem could not be supplemented witha single- characteristic using parameter design problem. Thus, in this paper, I will analyze a plant system which is run in manufacture in today's world, and then find out factors that affect production time and failure rate with correlation inn plant operation. I will also show optimal design method that can minimize production time and failure rate using multi characteristic robust design method in plant system.