tailieunhanh - Business process improvement_4

Tham khảo tài liệu 'business process improvement_4', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Confounding also called aliasing ENGINEERING STATISTICS HANDBOOK hW tools raids lỉEÂtCH BACK Nixf 5. Process Improvement . Choosing an experimental design . How do you select an experimental design . Fractional factorial designs . Confounding also called aliasing Confounding means we have lost the ability to estimate some effects and or interactions Sparsity of effects assumption One price we pay for using the design table column X1 X2 to obtain columnX3 in Table is clearly our inability to obtain an estimate of the interaction effect for X1 X2 . C12 that is separate from an estimate of the main effect for X3. In other words we have confounded the main effect estimate for factor X3 . C3 with the estimate of the interaction effect for X1 and X2 . with C12 . The whole issue of confounding is fundamental to the construction of fractional factorial designs and we will spend time discussing it below. In using the 23-1 design we also assume that C12 is small compared to C3 this is called a sparsity of effects assumption. Our computation of C3 is in fact a computation of c3 ci2. If the desired effects are only confounded with non-significant interactions then we are OK. A Notation and Method for Generating Confounding or Aliasing A short way A short way of writing X3 X1 X2 understanding that we are talking of writing about multiplying columns of the design table together is 3 12 factor column similarly 3 -12 refers to X3 -X1 X2 . Note that 12 refers to column multiplication multiplication of the kind we are using to construct the fractional design and any column multiplied by itself gives the identity column of all 1 s. Next we multiply both sides of 3 12 by 3 and obtain 33 123 or I 123 since 33 I or a column of all 1 s . Playing around with this algebra we see that 2I 2123 or 2 2123 or 2 1223 or 2 13 since 2I 2 22 I and 1I3 13 . Similarly 1 23. http div898 handbook pri section3 1 of 3 5 1 2006