Robust Box-behnken Design With Missing Data

Box-Behnken design is a three-level design that combines factorial design and incomplete block design,and is a second-order design that uses more.If the data is missing in the experiment,it will affect the robustness of the experimental design and have a certain impact on the results of the data analysis.If the impact on stability is small,you can continue to use the original design,and if the impact is large,the original design is not applicable.In view of the above problems,this paper explores the robustness of the missing data of the Box-Behnken design,"quantifies" the robustness,measures the robustness by the relative prediction of variance expansion,and uses specific values as references to determine whether the original design can continue to be used.In this paper,we first study the predicted variance when a single data is missing in a Box-Behnken design,and use the prediction variance to derive a mathematical formula for the expansion of the relative predicted variance.According to the formula,the amount of expansion of the relative predicted variance depends not only on the length of the given vector and the length of the vector of the missing observation and the angle between these two vectors,but also on the sum of the squares of the inner product of the two vectors.Subsequently,the magnitude of the relative predicted variance expansion and the distribution of variables within 5% and 10%,respectively,are given in detail by sub-case.Finally,the specific values of the relative prediction variance expansion at 5% and 10% are listed in the form of a table when the number of factors is 5,6,and 7.