Two-level factorial and fractional factorial designs in blocks of size two .1NORM Coal Two-Level Factorial and Fractional Factorial Designs in Blocks of Size Two NORMAN R.DRAPER University of Wisconsin,Madison,WI5706 IRWIN GUTTMAN University of Buffolo,Buffalo,NY 14214-3000 the tradonmthod tomm When two-level d s but stil using blocks of si two.al isisuseful to ow in sit tothe Introduction the effects obtainable from the unblocked design can aturally.this requires more runs,as 2tEastorialLEatiatonswith only two machines were available.or there were great Two Factors acteris We discuss this specificallyn factorialadfiactionelacto of which coud be perfo Thus,six tw factorial efects.or effects combinations.that would choice design,and uuhered d.2)d.3).0 2 3).12.D.and erent block changes in levels).Thus.in particular,there are no ver.we could get a blocks interactions of blocks with factors. ond run of the pair,are commonly used in block C2=-1C13=6一功C14=y4-1 hewo.bu C23=-欢24=4-欢4=4- block effects.If more blocks are used.however,all sav.can then be written as 2弘1=-1+h-+=c12+c3=c14-c2 22=-1-+班+=G3+c24=c14+c23(2) Dr.Guttman is a Professor of Statistic 212=1一2一+4 -C12十C34 一C3十24 Vol.29.No.1.January 1997 71 Journal of Quality Technology Reproduced with permission of the copyright owner.Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Two-level factorial and fractional factorial designs in blocks of size two Draper, Norman R; Guttman, Irwin Journal of Quality Technology; Jan 1997; 29, 1; ABI/INFORM Global pg. 71