Three‐dimensional sequential uniform design

Abstract

PurposeThe purpose of this paper is to extend two‐dimensional sequential uniform design and present three‐dimensional sequential uniform design which can optimize the problem of determining the extreme value of three‐factor polynomial.Design/methodology/approachSince there are limitations in two‐dimensional sequential uniform design, three‐dimensional sequential uniform design introduced in this paper is to arrange the experimental points by U9(93) uniform design table and to determine the maximum of the experimental values according to the demand. It is proven that the convergence of the experimental central point's sequence and that it can optimize the problem of determining the extreme value of no‐cross term quadratic polynomial monotone function class and the corresponding conditions are also proven. Taking the no‐cross term quadratic polynomial monotone function as an example, the superiority of it is testified.FindingsThree‐dimensional sequential uniform design can optimize the problem of determining the extreme value of three‐factor polynomial. It can get higher precision and better convergence but do fewer experiments than general uniform design.Practical implicationsA very effective method in resolving the problem of selecting optimum on multi‐dimensional space.Originality/valueA new method of three‐dimensional sequential uniform design which can get higher precision and better convergence is presented.