I am trying to construct a fractional factorial design by the screening design platform，and the design I want to make is a 2（5-1）design with the generator of I=ABCD.this is not a abbreviation design，so I want to change the generator from ABCDE to ABCD.but it looks impossible to generate this design by change the generating rules in screening design platform.
if I dont click any of them I get a design which all runs with a positive E level.if Iclick all I get a abbreviation design with generator I=ABCDE
Accepted Solutions
Hi @ZHANDOUJI,
@statman gave a really good answer so I won't discuss the points he mentioned.
Some complementary remarks :
- When dealing with fractional factorial design, the fractional reduction gives an indication about the number of generators required. For example, a 2^(5-1) will require 1 generator as mentioned in the naming (and enabling to divide the number of runs by 2).
More generally, the naming 2^(k-p) explicitly mention the number of factors k and the number of generator p which enable you to understand the reduction of the number of runs : runs number = total number required for a full factorial design (2^k) divided by 2^p - When using generators to create fractional factorial designs, the general recommendation is to use the longest generator first, as it enables to have the highest resolution for your design. It also enables to respect Effect Hierarchy.
In your case with 5 factors, the generator described by I = ABCDE enables to have a resolution V design : No main effect or two-factor interaction is aliased with any other main effect or two-factor interaction, but two-factor interactions are aliased with three-factor interactions. This can be seen easily through "manipulations" of the generator (like mentioned by @statman) to visualize the aliasing of effects :
I = ABCDE -> A = BCDE, so main effects A is confounded with 4-factors interaction BCDE
I = ABCDE -> AB = CDE, so 2-factors interaction AB is confounded with 3-factors interaction CDE
Note that this resolution generator methodology also avoids confounding between hereditary terms, like interaction ABC and main effect A for example (which would otherwise be linked to a poor resolution II generator described by I = BC and the aliasing of main effects B and C !). - By default, JMP tries to find the highest resolution generator depending on the number of factors and reduction you have described. Note that you can still change the proposed generator and finds another one by checking the cases. For example, instead of resolution V generator described by I = ABCDE, I can also use the generator I = ABCE (equivalent to your generator I =ABCD, resolution IV: No main effects are aliased with two-factor interactions, but two-factor interactions are aliased with each other.) by dechecking the case DxE :
If you order your factors like ABCED, you can propose the generator I = ABCD by dechecking the case ExD :
However in this situation, I don't know what would be the benefit of using a resolution IV generator when you could use a resolution V generator ?
On a side note, if you're using fractional factorial designs for real industrial use case, I would also recommend trying Custom Designs platform or choosing the option "Create a Main Effects Screening Design", as the aliasing structure can be different and may avoid complete confounding of effects, depending on the run size specified and assumed model, example with a main effects screening design with 16 runs and 5 factors like in your example :
More infos about fractional factorial designs, generators and design resolution : 5.3.3.4.4. Fractional factorial design specifications and design resolution
Lesson 8: 2-level Fractional Factorial Designs
Resolution in Screening Designs
Hope this complementary answer will help your understanding,
Hi @ZHANDOUJI,
@statman gave a really good answer so I won't discuss the points he mentioned.
Some complementary remarks :
- When dealing with fractional factorial design, the fractional reduction gives an indication about the number of generators required. For example, a 2^(5-1) will require 1 generator as mentioned in the naming (and enabling to divide the number of runs by 2).
More generally, the naming 2^(k-p) explicitly mention the number of factors k and the number of generator p which enable you to understand the reduction of the number of runs : runs number = total number required for a full factorial design (2^k) divided by 2^p - When using generators to create fractional factorial designs, the general recommendation is to use the longest generator first, as it enables to have the highest resolution for your design. It also enables to respect Effect Hierarchy.
In your case with 5 factors, the generator described by I = ABCDE enables to have a resolution V design : No main effect or two-factor interaction is aliased with any other main effect or two-factor interaction, but two-factor interactions are aliased with three-factor interactions. This can be seen easily through "manipulations" of the generator (like mentioned by @statman) to visualize the aliasing of effects :
I = ABCDE -> A = BCDE, so main effects A is confounded with 4-factors interaction BCDE
I = ABCDE -> AB = CDE, so 2-factors interaction AB is confounded with 3-factors interaction CDE
Note that this resolution generator methodology also avoids confounding between hereditary terms, like interaction ABC and main effect A for example (which would otherwise be linked to a poor resolution II generator described by I = BC and the aliasing of main effects B and C !). - By default, JMP tries to find the highest resolution generator depending on the number of factors and reduction you have described. Note that you can still change the proposed generator and finds another one by checking the cases. For example, instead of resolution V generator described by I = ABCDE, I can also use the generator I = ABCE (equivalent to your generator I =ABCD, resolution IV: No main effects are aliased with two-factor interactions, but two-factor interactions are aliased with each other.) by dechecking the case DxE :
If you order your factors like ABCED, you can propose the generator I = ABCD by dechecking the case ExD :
However in this situation, I don't know what would be the benefit of using a resolution IV generator when you could use a resolution V generator ?
On a side note, if you're using fractional factorial designs for real industrial use case, I would also recommend trying Custom Designs platform or choosing the option "Create a Main Effects Screening Design", as the aliasing structure can be different and may avoid complete confounding of effects, depending on the run size specified and assumed model, example with a main effects screening design with 16 runs and 5 factors like in your example :
More infos about fractional factorial designs, generators and design resolution : 5.3.3.4.4. Fractional factorial design specifications and design resolution
Lesson 8: 2-level Fractional Factorial Designs
Resolution in Screening Designs
Hope this complementary answer will help your understanding,