品質(zhì)管理相關(guān)知識(英文版)(編輯修改稿)
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【文章內(nèi)容簡介】 n: IV Runs: 8 Replicates: 1 Fraction: 1/2 Blocks: none Center pts (total): 0 Design Generators: D = ABC 9 Belton Confidential: For training only Alias Relationships As mentioned earlier, the pattern of levels for factor X4 in first example is identical to the pattern of levels for the interaction X1X2X3. X4 and X1X2X3 are called aliases of each other. An alias is an individual factor or interaction whose pattern of levels in an experiment is identical to that of another factor or interaction. 10 Belton Confidential: For training only Alias Relationships In a fractional factorial design, every individual factor and interaction has an alias. The calculated effect of any factor or interaction is an estimate of the sum of the effects of the aliased variables, . the calculated effect of X4 (or of X1X2X3) is an estimate of the sum of the effects of X4 and X1X2X3. The effect of the factor X4 is said to be confounded with the effect of the X1X2X3 interaction. 11 Belton Confidential: For training only Example For the 241 fractional factorial design in Example 1, determine the alias for each factor and interaction. Note : X4 = X1 X2 X3 , . X4 is generated from X1 X2 X3 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 1 112 Belton Confidential: For training only Example From X4 = X1 X2 X3 Multiply both sides by X4, X4 X4 = X1 X2 X3 X4 I = X1 X2 X3 X4 (1) (Note : Xi Xi = I ? 1) Multiply both sides of (1) by X1, X1 = X1 X1 X2 X3 X4 = X2 X3 X4
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