Hi @AHM,
Welcome in the Community !
Regarding the treatments you would like to have, why not considering a DoE with two factors :
- X1 : Quantity of NPK (with levels at 0 and at "normal/standard" quantity), numeric continuous factor
- X2 : Quantity of new fertilizer (with levels at 0, middle level and high level), numeric continuous factor.
Using a standard factorial approach, and specifying a model with the two main effects, a quadratic effect for X2 to have experimental runs with 3 possible levels ( if you want to have 4 levels for factor X2 : absence, low, middle and high levels you can specify a cubic order effect term in addition in the model) and the interaction between these two factors, you should have all the treatments you are expecting :
You can create this Custom Design with this script (you can modify the quantity levels used, I just used them for illustration):
DOE(
Custom Design,
{Add Response( Maximize, "Y", ., ., . ),
Add Factor( Continuous, 0, 5, "NPK Quantity", 0 ),
Add Factor( Continuous, 0, 10, "New fertilizer quantity", 0 ),
Set Random Seed( 14871954 ), Number of Starts( 312796 ), Add Term( {1, 0} ),
Add Term( {1, 1} ), Add Term( {2, 1} ), Add Term( {2, 2} ),
Add Alias Term( {1, 1}, {2, 1} ), Set Sample Size( 8 ), Simulate Responses( 0 ),
Save X Matrix( 0 ), Make Design}
)And datatable of the DoE (without replicates) is attached.
If you want to replicate the whole design 2 more times, you can use the "Augment Design" platform (in menu "DoE", "Augment Design"), click on "Replicate" option and specify 3 as the number of replicates :
You'll end up with a completely randomized design with 3 replicates, for a total of 24 runs (datatable attached).
If you have constraints about number of runs done per day for example, you can use blocks in the initial design generation, by adding a factor (type blocking) and specify the number of runs per block :
You can then specify the same model as before (with added block effect), the number of runs in total (24), and you'll end up with a design in 3 blocks (see datatable attached).
I hope these design options may help you in the creation of your DoE,
With your informations, here is how the setting of the factors and model can be done in order to get the 8 treatments you need :
To obtain this 8-runs design, here is the script :
DOE(
Custom Design,
{Add Response( Maximize, "Y", ., ., . ),
Add Factor( Categorical, {"0", "NPK"}, "NPK", 0 ),
Add Factor( Discrete Numeric, {0, 5, 10, 50}, "GHQ", 0 ),
Set Random Seed( 1540555554 ), Number of Starts( 329553 ), Add Term( {1, 0} ),
Add Term( {1, 1} ), Add Term( {2, 1} ), Add Term( {2, 2} ), Add Term( {2, 3} ),
Add Term( {1, 1}, {2, 1} ), Set Sample Size( 8 ), Simulate Responses( 0 ),
Save X Matrix( 0 ), Make Design}
)Then, to have 3 replicates, you just need to use this design and go to "Augment Design", option "Replicate", specify that you want each runs done 3 times, and you'll obtain your 24 runs as needed (datatable attached). The script used to augment the design is :
dt = Current Data Table();
dt2 = dt << run script( "Original Data Table" );
Current Data Table( dt2 );
DOE(
Augment Design,
X( :NPK, :GHQ ),
Y( :Y ),
{Augment Method( Replicate, 3 ), Save X Matrix( 0 ), Simulate Responses( 0 ),
Make Table}
);Note that you can find these scripts and modify them in every DOE datatable, by right-clicking on the green triangle next to "DOE Dialog" and then clicking on "Edit". This will open a windows with the script used to generate the design.
Hope this answer will help you,