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1 1 110 1 1 1 1 1 1 1 1 1 1 1 1 1 1 111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 112 1 1 1 1 1 1 1 1 1 1 1 1 1 1 113 1 1 1 1 1 1 1 1 1 1 1 1 1 1 114 1 1 1 1 1 1 1 1 1 1 1 1 1 1 115 1 1 1 1 1 1 1 1 1 1 1 1 1 1 116 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 Belton Confidential: For training only Example The set of 8 runs for which X1X2X3X4 = 1 is shown below: It can be seen that the pattern of levels for factor X4 is identical to the pattern of levels for the interaction X1X2X3. In fact, for this design the pattern of levels for every individual factor and interaction is identical to one other individual factor or interaction. Run X 1 X 2 X 3 X 4 X 1 X 2 X 1 X 3 X 1 X 4 X 2 X 3 X 2 X 4 X 3 X 4 X 1 X 2 X 3 X 1 X 2 X 4 X 1 X 3 X 4 X 2 X 3 X 4 X 1 X 2 X 3 X 41 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 13 1 1 1 1 1 1 1 1 1 1 1 1 1 1 14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17 1 1 1 1 1 1 1 1 1 1 1 1 1 1 18 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16 Belton Confidential: For training only Fractional Factorial Design The design in last example is called a 241 fractional factorial design, where 2 = number of levels for each factor 4 = number of factors 1 = degree of fractionation of the corresponding full factorial design (in this case 21 = 189。 of the corresponding 24 factorial design) The general notation for a 2level fractional factorial design is 2kp, where 2 = number of levels for each factor k = number of factors p = degree of fractionation, or number of generators 7 Belton Confidential: For training only Example Stat ? DOE ? Factorial ? Create Factorial Design 8 Belton Confidential: For training only Example Factorial Design Fractional Factorial Design Factors: 4 Base Design: 4, 8 Resolutio