Robust Parametric Split-plot Design With Minimal Low-order Confounding

Robust parameter design(RPD)is an engineering methodology for reducing the variation of a product or a process.If the noise factors and control factors in such a design are treated as the whole plot(WP)factors and subplot(SP)factors,then fractional factorial split-plot(FFSP)design can be used.In RPD experiments,the effects of primary interest are the control factor main effects,the control-by-noise factor interactions and control-by-control factor interactions.Performing the experiment as a split-plot design allows the significance of effects of particular in-terest to be assessed with more power than a completely randomized design.The paper proposes a new optimal criterion for selecting FFSP designs in the robust parameter design circumstances,that is,the minimum aberration of subplot type(SP-MA)criterion.The construction theory of SP-MA FFSP designs with k1=0 or k2=0,k1=1 and k2=1,2,3,k1=2 and k2=1 is studied.The SP-MA FFSP designs with 8,16 and 32 runs are tabulated in Appendix.The paper introduces the research significance of design of experiments,it is explained that under what conditions the FFSP designs can be used.Some research results that relate to minimum aberration(MA)and FFSP design are given.The definitions of full design,fractional factorial design and FFSP design and some commonly used optimality criteria are reviewed.As a basis of constructing SP-MA FFSP designs,we give the construction method of the MA 2n-k designs.The paper proposes the effect hierarchy principle of the FFSP-RPD and the SP-MA criterion and introduces some useful results in robust parameter design circumstances.Let Ai,o(d)and Ai,1(d)be the numbers of WP type defining words and SP type defining words with length i,respectively.Define the following two n-dimensional sequences W1(d)=(A1,1(d),A2,1(d),A3,1(d),…,An1,1(d),…,An1+n2,1(d)),W22(d)=(A1,0(d),A2,0(d),A3,0(d),…,An1,0(d),0,…,0),where n=n1+n2.The design which is obtained by sequentially minimizing W1(d)and W2(d)is called SP-MA design.Then we study the construction theory of SP-MA FFSP designs with k1=0 or k2=0,k1=1 and k2=1,2,3,k1=2 and k2=1 and get the corresponding optimal design.Finally,we give a summary and compare SP-MA designs with the designs given in literature[6].