# Runs don't change in a strip plot DOE when hard to change factors changes are not independend from very hard factors?

[#1]

I have a strip plot DOE with 2 very hard and 2 hard to change facors, also 2 are easy to change. With my model I get 8 whole plots and 16 subplots with 48 runs However when I don't allow the hard to change factors to change independend from very hard the number of runs remain the same? Allowing all whole plot x subplot conbinations should give significantly more runs?

[#2]

Hi @frankderuyck,

The option you're mentioning "Hard to change factors can vary independently of Very hard to change factors" during design creation will only influence the randomization and design structure, depending if the Very hard to change factors can vary independently from Hard to change factors (Two-Way Split Plot designs), or if Hard to change factors levels are nested within the Very Hard to change factors levels (Split-Split Plot designs).
See more explanations about randomization restrictions in designs.

The number of runs is influenced by the total number of runs, the number of whole plots and subplots. Of course, depending on the restriction randomization, the power for main effects and other higher order effects won't be the same between the two scenarii you mentioned : the more constraint on randomization, the lower the power for main effects of the factors affected by this randomization restriction.

Hope this answer will help you,

[#3]

Hi Victor, this is a process in two steps, 2 factors in first and 4 in second step; according to my model I have 8 plots (very hard to change step 1) and 16 subplots (hard to change in step 2) so if hard to change factors can't vary independent of very hard to change factors one will require all 8 x 16 combinations = 128 runs correct? However, when I chose this option the number #runs = 48 i.e .default #runs for a strip plot DOE with hard to change independent of very hard to change?

[#4]

No, you don't need to test all combinations. Let's start from the beginning:

• You have two continuous 2-levels factors for the first step, so 4 individual combinations possible. With 8 whole plots, it allows you to replicate some treatments (and increase the number of degree of freedom).
• Then you have four continuous 2-levels factors in the second step, so 16 individual possible combinations. You don't need to run all of them (depending on your assumed model), but the number of subplots you have specified allows it to test them all.

Depending on the model complexity (number of terms) and number of whole plots and subplots, JMP will calculate a recommended number of runs that is a multiple of the whole plots and subplots number. For all main effects and interaction effects, you need 1 (intercept) +6 (main effects)+15 (2-factors interactions) = 22 degree of freedom (minimum required). I guess you could run your design with 32 runs, as it is a multiple of both 8 and 16, but you can choose any number multiple of 16: 32, 48, 64, 80, 96, ... However it might be safer to have higher number of runs, as you will be able to estimate whole plots (7) and subplots (15) effects. So if you sum these effects to the previous model effects, 48 runs is a good choice and allow some degree of freedom for the 44 terms to estimate.

Hope this answer clarify,

[#5]

Perfect Victor, this is very clear thanks, however I don't understanstand why there is an option to choose - you can check this box above the Number of Whole plots - between dependent and independent very hard & hard factors, result is the same?

[#6]

As I explained in my first answer, this option will lead to different randomization restrictions, so different design structures with the same number of runs, whole plots and subplots.

• If Hard to change factors can't vary independently from Very hard to change factors, then the levels of Hard to change factors are nested within the levels of Very Hard to change factors (Split-Split Plot designs, 2 subplots per whole plots here) :
  
  
• If Hard to change factors can vary independently from Very hard to change factors (option checked), then the levels of Hard to change factors are randomized within the levels of Very Hard to change factors (Two-Way Split Plot designs, 6 subplots per whole plot here) : 

Hope the answer is clearer now :)

[#7]

Hi Victor, think there is a misunderstanding, what you mention above is what I would expect when I switch to option hard & very hard to be dependent; however  # wholeplots, #subplots and #runs all stay the same? Indeed when I go to make DOE I get the message that I need more whole plots; so yes all # here above had to change, strange, why did it not?

[#8]

Can you please describe more precisely your design setup and share the design script or the JMP table ?

With your settings as described, 2 Very hard to change continuous factors and 4 Hard to change continuous factors, 8 whole plots and 16 subplots with 48 runs, with or without the option of dependance between very hard and hard to change factors, I can create a split-split plot or a two-way split plot design without problem. Sometimes JMP may change the values of subplots/whole plots/runs depending on the options you have chosen based on heuristics, but if the design is possible with enough degree of freedoms, you can change these values without problems. Try to check/uncheck the option about very hard and hard to change factors dependance before changing the values, there seems to be some bugs.

Here the script for the Split-Split Plot design with 48 runs, 8 whole plots, 16 subplots situation with no independant variation between very hard and hard to change factors:

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ),
	Add Factor( Continuous, -1, 1, "X1", 2 ),
	Add Factor( Continuous, -1, 1, "X2", 2 ),
	Add Factor( Continuous, -1, 1, "X3", 1 ),
	Add Factor( Continuous, -1, 1, "X4", 1 ),
	Add Factor( Continuous, -1, 1, "X5", 1 ),
	Add Factor( Continuous, -1, 1, "X6", 1 ), Set Random Seed( 1232803225 ),
	Number of Starts( 312 ), Add Term( {1, 0} ), Add Term( {1, 1} ),
	Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {4, 1} ), Add Term( {5, 1} ),
	Add Term( {6, 1} ), Add Term( {1, 1}, {2, 1} ), Add Term( {1, 1}, {3, 1} ),
	Add Term( {1, 1}, {4, 1} ), Add Term( {1, 1}, {5, 1} ),
	Add Term( {1, 1}, {6, 1} ), Add Term( {2, 1}, {3, 1} ),
	Add Term( {2, 1}, {4, 1} ), Add Term( {2, 1}, {5, 1} ),
	Add Term( {2, 1}, {6, 1} ), Add Term( {3, 1}, {4, 1} ),
	Add Term( {3, 1}, {5, 1} ), Add Term( {3, 1}, {6, 1} ),
	Add Term( {4, 1}, {5, 1} ), Add Term( {4, 1}, {6, 1} ),
	Add Term( {5, 1}, {6, 1} ), Set N Whole Plots( 8 ), Set N Subplots( 16 ),
	Set Sample Size( 48 ), Optimality Criterion( "Make A-Optimal Design" ),
	"A-Optimality Parameter Weights"n(
		[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
	), Simulate Responses( 0 ), Save X Matrix( 0 ), Make Design}
);

And here the script for the Two-Way Split Plot design (also called "Strip plot" and visible in the script) with 48 runs, 8 whole plots, 16 subplots situation with independant variation between very hard and hard to change factors:

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ),
	Add Factor( Continuous, -1, 1, "X1", 2 ),
	Add Factor( Continuous, -1, 1, "X2", 2 ),
	Add Factor( Continuous, -1, 1, "X3", 1 ),
	Add Factor( Continuous, -1, 1, "X4", 1 ),
	Add Factor( Continuous, -1, 1, "X5", 1 ),
	Add Factor( Continuous, -1, 1, "X6", 1 ), Set Random Seed( 868486588 ),
	Number of Starts( 341 ), Add Term( {1, 0} ), Add Term( {1, 1} ),
	Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {4, 1} ), Add Term( {5, 1} ),
	Add Term( {6, 1} ), Add Term( {1, 1}, {2, 1} ), Add Term( {1, 1}, {3, 1} ),
	Add Term( {1, 1}, {4, 1} ), Add Term( {1, 1}, {5, 1} ),
	Add Term( {1, 1}, {6, 1} ), Add Term( {2, 1}, {3, 1} ),
	Add Term( {2, 1}, {4, 1} ), Add Term( {2, 1}, {5, 1} ),
	Add Term( {2, 1}, {6, 1} ), Add Term( {3, 1}, {4, 1} ),
	Add Term( {3, 1}, {5, 1} ), Add Term( {3, 1}, {6, 1} ),
	Add Term( {4, 1}, {5, 1} ), Add Term( {4, 1}, {6, 1} ),
	Add Term( {5, 1}, {6, 1} ), Make Strip Plot Design, Set N Whole Plots( 8 ),
	Set N Subplots( 16 ), Set Sample Size( 48 ),
	Optimality Criterion( "Make A-Optimal Design" ),
	"A-Optimality Parameter Weights"n(
		[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
	), Simulate Responses( 0 ), Save X Matrix( 0 ), Make Design,
	Set Run Order( Keep the Same ), Make Table}
);

The error message you see about whole plots appears for a different reason, when the number of whole plots is equal to the number of terms in the model for the very hard to change factors. If I specify in your example 4 whole plots with 16 subplots for 48 runs, the message error appears, because I need to estimate 1 intercept, 2 main effects and 1 interaction effect for the very hard to change factors (4 terms in the model), so there is no degree of freedom left in the whole plot structure to estimate the whole plot variance (at least one more whole plot is needed, si 5 whole plots in total minimum). If the number of whole plots is inferior to the number of terms in the model for the very hard to change factors, JMP automatically changes the value to the minimum value possible (# whole plots = number of terms in model for very hard to change factors).

Hope this answer will clarify some doubts, please share more infos and JMP table if this answer doesn't solve your problem,

[#9]

In order to better clarify the problem find In attachment a JMP file "FACTORS STRIP PLOT" with the DOE factors and a ppt with the DOE results & problem description; hope this is sufficiently clear?

As for the model: no need to estimate the effects Q², Fl*P, c*p and c*Fl

[#10]

Ok, I see better.
The error message concerns this time the subplots and not the whole plots structure :

• The whole plots structure is adapted, as you need for your configuration up to 6 degree of freedoms to estimate the intercept (1 DF), the 2 main effects (3 DFs because one of the main effect is linked to the three-levels categorical factor, so 2 DFs are needed), and the interaction between the two very hard to change factors (2 DFs because of the three-levels categorical factor).
  In total you need 6 DFs, so with 8 whole plots the situation is OK. I just checked by lowering the number of whole plots to 6, and I see two error messages in this situation: one for the whole plot (because not enough DFs to estimate whole plot variance), and one for the subplots (in the case when the very hard and hard to change factors cannot vary independently).
  
  
• In the subplots structure, you need 16 DFs if you're using a RS model without some terms removed like you mentioned (and if my calculations are correct): 2 DFs for the main effects of hard to change factors, 6 DFs for the interactions between hard to change and very hard to change factors, 2 DFs with the easy to change factors, and 2 DFs for the quadratic effects of the hard to change factors. You then have to add 2 DFs for the main effects and 2 DFs for the quadratic effects of easy to change factors, so total = 16 DFs required.
  • If the very hard to change and hard to change factors can't vary independently, you'll have only 16 individual and independant "group" of observations (2 different subplots per whole plot), so that leaves no DFs to estimate subplot variance.
  • If they can vary independantly, you'll see that the design structure allocates the subplots randomly to the whole plots, which greatly increases the DFs to 48 (since there are no combinations  of whole plots x subplots "repeated" like in the "dependance" scenario), which is large enough to estimate the required model terms and subplots variance.

Hope this answer will clarify the different situations,