72 NORMAN R.DRAPER AND IRWIN GUTTMAN TABLE 1.22 Factorial Design Run No. 2 of 12 pairings may be preferable. aces like thseo 4 ted pairs (i.e. using any pairing ca only once So th a great fle We see from these equations that we need only four el r comparisons (c12. and c ges of the eub It is well k e each corner point.in a design which allows the runs to be estimated free a block to be performed in both orders in tead o 341).This and Obviously h2 is not then ob Figure 1(a).but using each ca twice. ainable I we chose use hemirrol Four or More Factors comparisons above (see Figure D could be used Because there are very many more choices as the that mumber of factors increases,it would be tedious to pair.how The set (e .a.,reguire changes of only one factor within a pairing Three Factors Similar calculations for three factors show that,of the 8 cts a (a) order. (Se Bo.(7. hernaitielycost and de ign）Many possible parisons on opposite faces.for example. k and (c) 56,c57,C66an0d EIGURE 1 The Lines a the Closed E: image points have the possible disadvantage that to sign Vol.29.No.1,January 1997 Reproduced with permission of the copyright owner.Further reproduction prohibited without permission.Reproduced with permission of the copyright owner. Further reproduction prohibited without permission