DARCY P.MAYS AND STEPHEN M.EASTER only a few design or process variables,replication of over the design locations to which runs can actually be allocated. ically.one shoule eneous variance structure.to cates The results that follow involve determining the designs that could be use optimal distribution of design points for a given het when dispersion effects exist.The remainder of the paper The mean models used in the ture and the degree of the variability.One problem timate these models are described.Then the vari mary of the y; process that an "educated stimate of the varianc ommendation s as to which designs should be used in structurecanbr certain situations. be estimated using either some preliminary data or Models and Designs The analysis presented as The experiment consists of N runs,which are allo estimate of the variance structure through previou ferent mean models are considered: ary to experiment a first order model- h=%+E11+2x21+4 Experimental designs are often evaluated with re adtstmationofparametens a partial second-order or interaction model =30+31x14+32x2+12x12+6:(2) oaKfdai2o91od mat design a second-order model: the 斯=风+1+22：+31212 alized variance of the regresio +31x1+32x2,+, (3) the design matrix and Wre the ji ar nting a weight or sion parameters,and the are random errors or e is kno own as integrated variance or I-optimality locations to which the be located. models,such as the fr orde two-level factorial des pre gion ()and N to be the total number of runs the effect inclding the interaction term (Box an in the experiment,the /-optimal design minimizes Draper(1987).H three-leve actorial c Ixw-ix)x that the different variance structures that are consid. trnce (XW-x)xx'dx ered can be implemented.The second-order model the thr In the analysis that follows the evaluation of this in natural choice in this case.It is important to note tegrated variance function is made by averaging only that a three-level factorial structure is used,but tha oual of Qualit Technolo) Vol.29.No.I.January 1997 Reproduced with permission of the copyright owner.Further repr du ction pro hibited without permission Reproduced with permission of the copyright owner. Further reproduction prohibited without permission