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the order that we defined in the table. In the table, this is not randomized. This here,
it follows the sequence 1, 2, 3, 4. If we execute, if we run this, this order here,
we are not ensuring randomization. So we must run first this set of conditions, then this
okay. First, for the randomization, the first experiment we should perform, it must be in
the following levels. The release angle here, it must be at 105. And the pin elevation here,
it must be at the lower level. Pin elevation at 100 here. So we put it at 105 and we drag
it and release. So here we have our first experiment. We have a value of maybe 70 and a half.
17 and a half. First condition, 105, 100, we got 70 and a half. Now let's go to the second condition.
Our second condition is held here. Release angle must be at 105 degrees and pin elevation must be at
185. So release angle at 185 maximum and the pin elevation remains at 100. So when we do this,
this is going to apply even more when we are in custom designs, when certain conditions of our
experimentation does not fit into a classical design. But let's go one step at a time.
Basically, let's see here how can we do an analysis procedure for the factor design.
The first thing is the estimate of the factor effect. So we begin by estimating the effects of each factor
that is involved in factory design. So basically for the two factor design we did earlier,
it's typically involving just a couple of the average response, just like I was trying to do
by hand. So after we formulate the model, we have to perform some statistical testing
and we refine the model just like we did here. We remove the non-significant variables and we get
an even better model. Since we know that interactions are significant, we now have a much improved model.
If we were to make predictions with this model, it would be much better than this one where we do
account for the interactions that we know that are significant in this case. So basically this is how
we interpret the effectorial design and it would be interesting if we could replicate the design
and redo to get a sense of how it would be improved, how the model could improve by
but I'll just introduce to you guys something important. Since we are already redoing, why not
a little bit more of complexity so that this this that we're doing it it teaches it can teach us
more. I want to introduce the principle of block in the catapult experiment because here
in this case there is no external conditions influencing our experiment. Here we basically
just execute it and things happen and just affect the response. So in real life,
it's not exactly like this. Blocking, it's in this situation that blocking arrives.
Blocking is a fundamental principle in design experiments and blocking actually helps researchers
to address nuisance variables which aren't included here yet.
But we are going to in order to approach it with reality. So nuisance variables are factors
that can potentially influence the outcome of the experiment.
The goal of blocking actually is to mitigate the impact of the nuisance variables. So in a
research lab, you guys are going to have a lot of nuisance variables that may
impact your experiment. If you do not block, the variability from this external factor is going to
influence your response. You might actually end up that the variables from the factors you're
trying to control and kind of nonsense but actually come from the outside. So by blocking,
the experiment is that only the experiment is going to handle this kind of thing.
One common approach to block is through the use of a randomized block design. So basically
when we are going to just erase this design and when we are going to create a design,
jump will give us the possibility of blocking. So basically each block contains the experimental
unit. It's the same to where things happen in the experiment. So basically by grouping the
experimental units into blocks, we can observe that any variability associated with nuisance
variables with external factors that we are not accounting for, they are controlled within each
block. The randomized complete block design allows researchers to conduct a complete
replicate of the experiment within each block. So I'll show you guys here how this happens.
So this means that treatments or conditions that they are tested within each block.
So this allows you to have an experiment that will provide you more accurate testing of the
treatment effects while controlling for the nuisance variables. So randomization is still
employed in each block and this is done to ensure that the assignment of the treatment
is unbiased and to reduce the potential for systematic errors. So how can we implement
block, how can we implement those kinds of variables, what situation would be a situation
Let's try to imagine that wind conditions are happening here. So when we actually execute
wind conditions, they can interfere in our experiment. So this way,
we cross block. There is no other way because we cannot control wind conditions. So wind conditions
can come in several forms. The order in which the final release angles and clean elevations are tested
within each wind condition is random. We cannot control. But our response variable is going to be
to suffer the effect of the wind. So let's think of the following way. We have different combinations
of final angles, release angles and clean elevations. So these are represented by the two levels of
So additionally, we have several wind conditions. And we have tests within each wind condition.
Let's pretend that each day we test the counterpoint in a different day. Each block is a different
day. So in each day we have different wind conditions that we cannot control. So we can
create a design here where
like this.
We would run a set of our experiments at the same day. It's like if we were traditional
and basically the other set we have, let's say we had two wind conditions
in another day. So we cannot control different wind conditions. But by boating the experience,
the design, we can make the calculations that will allow us to see this different
effect of wind. Is the wind too fulfilling in my experience? Yes or no? Is it significant?
By how much? That's basically the question we are trying to answer. So how would we do this?
We're going to have to make a little bit of that. We cannot get that from the wind. So basically
a column for the wind, the wind condition which we call block. We have fire angle,
and we have release angle and wind elevation. So we have to make it easier for us to
with this custom design platform. So if we were to incorporate wind
in our program to make it more complex, we would still manage to be better than this.
And we would have three continuous factors, release angle, bungee position, and wind elevation.
I'll leave it to code. I talked about coding variables. If it's necessary, I can code it again.
I think it wasn't very clear. And now we have something else. We have a blocking
which is the wind that we cannot control. So here we will choose two runs per block.
Since we're doing a three factor experiment, we are going to have at least eight runs here.
So we are choosing to block. Let's do the custom design. Four runs per block. This is going to
give me two days basically. So we have here the wind condition.
And when we generate, we ask John to generate for us to see the response. And here is the problem.
Now it's correct. He was trying to define the number of runs by itself, but we are
trying to make eight runs. And the wind, we have account for two days. So we have three factors
and one blocking factor, which actually is the wind. Actually it's not the wind, it's the day,
because we cannot control the wind. We can only control the day. So we're performing the experiment
one day, and then we're performing the experiment another day to test different wind conditions for
our catapult experiment. So basically we asked John to make the design, and he will show us
how it's going to be. And you can see it already randomized for us. It said
plus one is the highest factor and minus one is the lowest factor. I could have
addressed the values here. So here's what it's randomized. So we would have to perform the
experiments. And one day, these specific experiments and these specific experiments are not the day.
So as we can see here, the power analysis is not very good because we actually
are cutting in half the experiment. We are analyzing a full factorial with three variables.
We actually are cutting in half the experiment. So basically when we make the table,
we account for... we have our experiment table and we can perform the experiment.
So basically we would run this experiment here on this set of conditions. And for our class here,
we would have to create specific conditions in our response here. Since we are in a virtual
environment, we basically perform the experiment in this order. And we would maybe, just so we can
see the effect, we would... for each response, we are going to insert some amount of...
we are adding some random amount to contribute to the response value, just as if we influenced
the response. So if we do this here, release angle, let's follow here. Release angle,
the first experiment task is low, low, high. So release angle, punch position,
the punch position is low as it's minimum. The pin elevation is at high value. Release angle is at
low value. Low value, I'll use 105. So okay, that's the response. So 61 to 62 and a half.
What I mean here is that without external conditions, this would be our response, right?
62 and a half. But since we are kind of trying to account for the external variability,
let's say that on day one, the wind was acting to the contrary
of the projectile. So let's assign here a value of that subject by two and a half. So
this is a simulation. If it were a real experiment, the result would come naturally, right?
You throw the ball, the wind acts upon it and it delays or speeds it up. So here we just simulated
the wind acting over the projectile. So let's say here, so we know what we're doing.
I'll call it wind effect. Basically, head value negative two and a half. So it will actually
the distance we get. So if we do it again, low high low,
release angle, bunch position, pin elevation. Bunch position now is at its highest value,
pin elevation here and release angle still at the lowest value. Well, here we have a value of 71,
two, three. Let's say we are at the same day at this moment, wind effect,
it didn't have any effect in our response. So when we threw the ball, the wind didn't act upon it.
So it remained at a value that it would remain. There was no wind. So basically,
the third round of experiments is low high here. At this moment, I have 289 here, but
let's say that this day the wind was backing, delaying the
but this time a little bit harder just for the same reason. So I'll just repeat again.
I think I haven't replicated this.
Let's say that another.
Look, I have already hit the mark where we are on the second day. So this day here, we
we must be
strong behavior for the wind. So basically, let's say that this day we
let's just increase it. So instead of increasing it more, 300.
High, low, low.
So with that,
and the last one.
Okay, 95.
So this analysis here, we are going to introduce the wind effect. So I don't know
so we could we can leave the analysis to after the lunch break. You guys want, what do you think?
Okay, then I'll see you guys. How much time do you do?
One hour is okay.
45 minutes. So I'll see you guys here in 45 minutes. You guys are at noon right now.
Here is 1330.
It's what a 30 or 50 PM. So see you guys.
At 2 15 here, it would be over there. Okay.
Have a good lunch, guys.
Okay. We can see the diagram with our yield versus extrusion pressure.
And we can use a red triangle to look at our Nova.
In large.
Very good. Thank you.
Welcome back.
Hope you all had a good lunch.
Just wait a few more minutes to see if any of you are
because yes, I went through the
there are there are more than one way to do it. Let me see.
So let's see. You've generated the full factorial design, right? So
the easier method to account for blocking. There's the manual method.
You go there.
Here. You can have it.
And then you have custom design is the first.
Custom design actually is a very handy part of job where you can fit
several types of situations into a design of a.
So instead of just.
The type of.
You can add three.
The block.
You've had your already.
So.
Yes.
You can go to.
And you can.
The number of factors.
You.
So now.
So.
Three very.
So when we are adding.
It kind of forces us to think.
Somewhat more or less.
How do we want to distribute this?
That's.
It's going to.
To.
Allow us to make a choice here.
How many runs we want to.
To have in this.
The custom design.
Allows you to.
He's it's more flexible so you could choose the minimum amount of runs for.
For this.
Note that this is a.
The expected amount of runs to cover the entire experimental space is actually.
So if you if you have.
All the possibilities then you have a full factorial design what have.
You won't have.
Problems you could replicate and have a two to the power of three experimental design and I replicate.
To improve the power of your experiment but is not required right but.
Here you can choose a minimum number of runs you probably make some calculations fraction.
And we try to create something that is called optimal design.
It's something a little bit more advanced but it's pretty handy because you can.
Your situation here.
Whether you have.
Continuous variable.
It's written in America.
Covery.
Uncontrolled several things it's pretty cool.
So when you do this.
In the case of blocking.
We specify that we want.
A.
So you know that we are getting a full factorial but we are adding a block.
Variable so actually.
There is another variable that it kind of kind of it's not control so you can choose here.
Two runs per block.
It's going to divide.
The the eight runs.
Into.
Four blocks.
Each block with two runs in our case I chose four because I was thinking two days.
We.
We would.
That's why I.
You see that it does.
Since we have.
Since we've.
It will basically.
That's the main difference between what.
You've done.
So.
Basically.
We did.
With plan.
The experience at the block the blocking the block factors.
And now it's up to us.
To try to analyze it here.
Try to.
So.
Now let's analyze the data and jump.
We've kind of simulated this in real life this doesn't exist does not exist.
Because the effect of the wind is going to be inherited.
Into the response that we are trying to tomorrow.
So the first day this distance is going to be if there is wind it's going to be.
Kind of.
Changed by itself because the wind is there so basically.
We've accounted that we defect here.
Just as a simulation and already.
That changed the value so how how could we analyze this we we've.
We organized the data.
The.
This is our.
So how how can we analyze this.
We came here.
To try to fit.
And basically.
Is a random effect right it's something we cannot control it's the wind and we want to know.
How much is it affecting the how much of the variability.
Are going to see in this analysis.
It corresponds to the.
To the.
To the wind.
So.
There are two ways we can proceed.
We can use the.
We can use here the fit by white white by X.
Platform or use the fit model platform.
Let's start the fit by fit white by X.
So we will enter.
The distance here is our response.
And our factors actually.
Three on the wrong keyboard yes.
I have three factors and we have a block a blocking.
Factor that's why we assigned it to the block.
To the block.
The block box here so we okay.
So jump.
This.
It's too zoom.
Okay.
So.
Jump provides us with the.
That includes the F.
So basically.
The F test statistics is accounting for the variability within each.
Wind condition within each day.
To we can also perform the most.
To identify significant significant difference between the factors.
So here basically.
Jump provides us with this.
A nova table here.
And finally we can analyze the.
We can access the residuals and we can chat here.
Showing that.
Basically the reason is significant factor.
The day is not significant for our core data at all.
So the blocking is is really.
See this this error.
It is here because of the.
The blocking factors protecting the experiment from.
From the.
If we had done the analysis without the.
The blocking factor.
This ability here only this error would be.
Inside our factors so this way we wouldn't be able to differentiate if the the factor.
The factor effect it was just because of the factor or it was.
For something else from the external so when we block the experiment.
We protect our experience from external factors and blocking is essential.
Is essential to block the every.
Is essential to develop a team for analyzing and.
Detecting a blocking factor in experiments because.
In several experiments one of the biggest.
Failures of failures.
A lot of experiments exactly because the experimenter.
Didn't block didn't block the.
His experiments so.
There's another way of analyzing block which is also treating it as a treating it.
As a random which is in this case it's really a random because we cannot control the winds.
And here we would do.
With we would come here in analyze fit model.
Realize that we are feeding a model.
With only three variables and the blocking variables for the blocking variable we are going to attribute a random.
Attribute.
So that jump changes the way it does the calculation now it's going to reuse the Ramo method.
So the Ramo method is.
To take into consideration.
When we run this you can see that.
Here our analysis.
You can see that 65.
Of the total variability it comes from the.
From the wind so if we didn't block.
This variability.
Would go into.
Experiment effect.
Another observation.
A running a running an eight.
Block design with four runs.
Just like we did here and running a full factory with two to the power of.
Represents two different.
I'm gonna say experimental setups in the context of design of experiments.
And there is the difference.
It's important for you guys to know that.
This as I was trying to say this.
Is a full factorial from the moment that we add the blocking.
So the.
It is the experimental runs they are divided into blocks as I was saying.
With each block containing like like a subset of the total number of runs.
So each one of these blocks consists of four runs we have two.
And that I thought of two blocks.
Two blocks.
So we think this is what I want you guys to understand that within each block.
All combinations of factor levels are tested at least once.
All combinations of factors are tested at least once.
This ensures that each factor level from in each factor level combination is represented in the experiment.
So.
This doesn't happen in the.
Eight run for factor design.
So the blocks are used to control for them for variability.
But there is a price to pay so.
It really helps to.
To.
It really helps to encapsulate the experiment.
But that might arise due to the factors.
I'm going to say outside of the experimental conditions.
So this design here.
This design it allows for the estimation of the main effects.
And the two factor interactions only.
It does not allow for the estimation of high or low interactions.
So in here.
If this were a full factor experiment.
We would have this.
We would have the opportunity to analyze.
All the high or low interactions present that are present in the two to the third.
Full factor.
And this is the main difference.
In the two to the third design.
All possible combinations of the factor levels are tested.
Here this.
The way this thing was distributed.
It allows.
For all possible combinations of factor levels to be tested.
But when we introduce the block.
This condition is lost.
We can only estimate.
Only two factor interactions.
And the main effects.
Which in most of the cases are.
Enough.
Depending on the speaker.
So the original full factor design.
It allows for the estimation of the main effects.
The two factor interactions.
And other high order interactions.
If there are any other orders.
And other high order interactions.
So the full factor obviously it provides a more comprehensive understanding of the relationship between factors and response variables.
Unlike the block design.
There is no blocking of runs.
So.
Each experimental run is independent of each other.
In here this doesn't happen.
These runs they are kind of trapped inside the block.
So we can only estimate.
We lose a little bit of information.
In summary.
While both designs involve eight experimental runs.
The block design.
With four runs only.
With four runs per block.
It focuses more on controlling the variability.
This is the focus of the block.
It focuses on controlling variability through blocking.
And it allows also to estimate strong effects.
Main effects.
And some two factor interactions.
On the other hand.
The full factor design.
Is going to explore all possible combinations.
But you guys already know that.
As we increase the number of factors.
To cover all this space.
It becomes pretty hard.
So basically.
We have some important in this type of.
The residuals.
They can be accessed.
Here.
Basically when you.
When you analyze the design on the model.
Jeff offers you the possibility.
To save.
The residuals.
Of the experiment.
And also to save the time.
To save the time.
To save the time.
To save the time.
Of the experiment.
And also the predicted values.
And other stuff.
So.
This would be.
To create a predictive model.
Out of this model.
Out of this model.
If we want to predict.
And.
Where the project is going to land.
Under the setting of conditions.
But.
What I'm highlighting here.
Is that you can access the residuals.
And the residuals.
In the context of design of experiments.
And statistical analysis.
They refer to the difference.
Between the observed.
And the values predicted by our model.
Right.
So they represent the basically.
Unexplained variability.
For our.
So how good is this model.
And basically the difference.
Between the observed.
And the predicted values.
Is the residual.
They are calculated basically by subtracting.
These predicted values.
From the observed values.
For each data point.
So.
You can do.
Interesting analysis.
With residuals to check for model.
And statistical.
Conformity.
I'll cover a little bit of this analysis.
More up front.
So.
This.
We have.
Something.
That is the.
Unreplicated.
The unreplicated design. Right?
What would be a.
A unreplicated design here.
In this case.
Basically.
If we had.
This 8-ground block design.
If you don't have.
Any replicates.
If you don't have replicates.
To show.
Basically.
You have an unreplicated design.
Where you cannot estimate.
The error.
Analyzing an unreplicated design.
Such as.
This we did here.
In the catapult experiment.
Can be a challenge.
Because this is due to the.
Number of data points available.
For estimation.
And also.
The interest. This is the disco interest.
If you don't collect the error.
You cannot estimate.
Very well the error.
You cannot estimate the.
The marginal value. Right?
In the case of the catapult experiment here.
An unreplicated design.
Would mean that.
Each combination of these factors here.
Is tested only once.
So basically.
If you consider the factors.
Release angle. Pin elevation.
Bunch position.
Each one of two levels.
Then.
An unreplicated design.
Because in this context.
It would actually involve.
Setting.
Setting up the catapult.
At each unique.
Combination.
And basically.
Only one measurement.
Or one observation.
Is taken for its combination.
So that's basically.
You cannot estimate the error.
So.
Because this means that this.
Is design. Is not.
We cannot perform an analysis.
And it. No.
We can still analyze it.
But.
It's a little bit different.
So.
Here's how.
We can perform an analysis.
With a.
Unreplicated design.
Well.
We try to fit model.
Here.
We're going to fit.
A model just like we did.
And basically.
We specify the model.
In this case here.
My random effect.
And here.
We.
Since we're talking about a.
Unreplicated design.
We have to generate.
Something that is called a.
Half ton of water.
So after we specify the model here.
We can navigate.
To the profile.
And.
We can try to.
Look for the.
And here. We want to generate.
Basically.
No.
So.
Basically.
Run.
Run.
The random.
Interfere.
Interfere.
Here.
It's pretty normal.
With the whole library of spinoffs.
A lot of variable.
Well I'm having a little bit of trouble.
Finding the.
The half normal.
Probability of what here.
I'll check.
And I'll get the answers to you guys.
But basically.
Basically.
The half normal plot.
Is going to allow you to.
To analyze the.
To analyze.
Every unreplicated design.
So.
Whenever you design.
Whenever you design.
Any.
Unreplicated.
Experiment.
There.
You plot the values.
Just.
Just like normal.
What happened to the plot.
You should be able to plot.
A normal plot here.
I'll investigate why.
I wasn't.
Being able to generate the plot.
In that other example.
Where we generated the custom DOE.
But when you generate.
A design here.
You.
And you create the model.
You have access to the.
To the normal plot.
So basically the normal plot here.
I missed something here.
Should be here.
Ah it's here.
It was underneath.
By.
The half normal plot.
The half normal plot.
Significant effects.
They are represented by.
Points that fall outside.
The reference line.
So when you generate.
The model. You come here and response.
And effect screening.
And you select the normal plot.
The normal plot of your model.
Should appear here.
And then since it's a.
Design.
We do the analysis by looking at the half normal plot.
So when we look at the half normal plot.
The points that fall outside.
The reference line.
They are considered to be.
Effects with a high.
A high significance.
Or they are important factors.
So.
Every effect that.
Extend beyond this line.
Is considered to be significantly significant.
So this indicates that.
The corresponding factor here.
Or the interaction.
It could be effect. It could be interaction.
It depends on the model.
Depends on the model parameters.
And every point.
That falls outside of this line.
It does have a significant impact.
Impact on the response.
Response back.
So after we identify significant effects.
Using the half normal plot.
The reference line.
Using the half normal plot.
You can perform additional analysis.
One of these analysis is the.
The multiple comparisons.
So basically.
You are going to be looking to the residuals.
And you are going to be further investigating.
The relationship between the factors.
And the response variable.
It's important to validate.
The results.
That you obtain.
And basically.
Every.
Every result obtained from.
A unreplicated design.
It's.
Or every design.
It's good to be validated.
So this point here.
They don't make sense because.
I've.
I've just through.
Random components here.
To show you.
Where.
What's the plan.
To access the normal plot.
And basically.
Then access the half normal plot.
So.
So.
So.
So.
So basically.
So.
So to analyze.
If we were to.
To execute.
Our experiment here.
Collect data.
And.
It happens to be.
A replicated design.
That would be the way we.
Should be analyzing.
The.
The design.
So let's think a little bit.
About the problem of.
The machine.
When we.
Create the design.
Basically.
We face that problem.
Of.
We use.
All of our variables.
All of our factors.
In the.
Catapult design.
Basically.
We would have five factors.
Five continuous factors.
These five factors.
When we continue.
If we were to.
To run.
A full factory design.
It would need 32.
Number of runs.
This is a huge number.
Even for a virtual environment.
So.
I wonder.
Any of you have.
I mean have you ever.
Encountered some situation where.
Certain factors.
Or conditions.
Consistently.
And might have.
Influenced.
Some experiments that you might.
So.
Basically.
Factors.
That are relevant.
And can be factors.
Not so much relevant.
So basically.
That's where.
We.
We start to.
If all these.
Are relevant.
As we.
Extend the catapult.
To.
To include these five factors.
Well the complexity.
In the experiment.
Increases significantly.
With each new.
Variable.
With each additional factor.
The number of possible combinations.
Of factor levels.
Includes exponentially.
This is belonging.
To a large number of.
We can see here.
32.
And basically.
It exhausts.
All the resources of.
Of most experiments.
So.
What can we do about this?
What if we need to analyze.
Seven.
More.
Seven.
Eight.
Ten factors at the same time.
The.
The experiment would continue.
To grow.
Explanation.
And if we would need to.
Apply any kind of replication.
It would double the size.
So basically.
What can we do about it?
To still investigate.
As much as we can.
Of a huge experiment like this one.
Well.
Basically this is the problem of.
The machine.
So.
Managing a larger.
Number of runs.
It presents.
A logistical challenge.
To the experiment.
Both.
In terms of resource.
Time.
And cost that.
Blars.
Have highlighted.
And basically.
Conducting a.
Run.
Run.
Is already.
So the number of.
Runs increase.
As the numbers.
The number of runs increases.
So does the complexity.
Of the data analysis.
So analyzing the results.
On significant factors.
Interactions become more challenging.
Particularly without the replication.
To estimate.
So.
Without this replication.
Things get even worse.
So the experiment.
May require more extensive resources.
Including.
Personnel.
Collection.
Equipment.
You name it.
Basically.
It can.
Drive an experiment.
It can stop.
It can stop an experiment.
From.
Finding.
The response.
Is looking for.
So.
When it comes to.
Multiple factors.
To maintain.
Experimental control becomes crucial.
And it's crucial.
Because.
We have to ensure reliability.
Reliability and reproducibility in our results.
So any value.
In experimental conditions.
Or external factors.
It could introduce unwanted variability.
It could also.
Affect the validity of the control.
So in summary.
Expanding the catapult experiment.
To find factors.
It introduces significant.
Complexity and challenges.
In our.
Our experience.
So.
We are trying to.
To replicate the design.
To the embedded statistical results.
In the catapult experiment.
To find factors.
The situation becomes.
Even more challenging.
When we try to replicate things.
So let's see the following.
Fraction of factorial designs.
Are actually.
A powerful.
And efficient tool.
That is used in experimental design.
Particularly when dealing with large numbers of factors.
In the context of the catapult experiment.
I invite you guys to explore.
How does the.
Fraction of factorial.
Would work here.
In our favor.
So.
Fraction of factorials.
Are the cornerstone of the screening design.
So.
Fraction of factorials.
Increases the size of factorials.
And.
The factor designs.
They.
To screen.
A large number of factors.
With fewer runs.
That's how we are going to be able to analyze.
A.
Seven factor.
Ten factor experiment.
And.
To find the factor.
Seven factor.
Ten factor experiment.
Basically.
The.
Designs.
They leverage.
The sparsity of effects.
This principle.
Is basically that.
Only a few factors.
So.
The four factor.
But.
Do we have to.
Do we have to cover the entire space.
Not always.
As I said before.
The focus.
Of fractional.
Is to be identifying the main factors.
And mostly the law over the interaction.
So.
The higher order interactions.
They don't.
Contribute much to.
Most of the system.
So.
This sparsity.
Effect is a principle.
A very important principle.
Of fractional factors.
So basically.
What happens when we.
When we.
When we try to execute a.
Experiment.
Let's say with five factors.
As a fraction.
Well. A few things happen.
There comes the concept of resolution.
And aliasing.
Because. Look at this table guys.
It's an interesting table.
A five factor experiment.
It would.
Require 32 runs.
This would be considered.
For fractional.
You would be able to.
To estimate.
All the factors.
And interactions.
And.
Basically.
The.
The situation.
Changed.
When you have to.
Add a block or a fractional factor.
If you.
If in this experiment.
Let's say that we.
Would have to add a block.
So.
To execute.
22 runs.
We could.
Do it.
By using.
A two block size.
Of 61 each.
And.
An eight block size.
A three.
Sorry.
A four block size.
With eight runs each.
And so on.
So.
Talking about fractional factorials.
They offer the possibility of.
Reducing half.
The number of runs.
We have.
To perform.
Without losing.
Without having to.
Drop the factors.
So to execute a.
16 run experiment.
We would have to.
We would need four factors.
To get a full factorial.
But we can analyze.
Five factors with 16 runs.
This.
Would allow us.
To estimate basically.
All two factor interactions.
And would be.
A design.
Of resolution five.
Resolution is a.
It's a term.
That is used basically.
To express.
It's the quality of that.
Of that fractional factorial design.
So fractional factorial designs.
They are.
Categorized into.
Different resolutions.
So resolution three designs.
The.
Alias.
They have something that is called.
So the many.
There are alias.
With all the two factor interactions.
In resolution three designs.
And the main effect here.
Is a resolution three design.
If we want to study.
Five factors.
And run only.
Eight runs.
We could do it.
We can do it.
But.
The only thing that we are going to be able to estimate.
Are the main effects here.
And this is going to be considered.
A resolution three design.
And also.
They are.
To be alias.
So you cannot estimate.
The two factor interactions.
So if you increase.
To 16 runs.
You increase the resolution.
Of the design.
So a design of resolution five.
For example.
It comes with fewer.
Alias.
Alias.
But.
It can become impractical.
So.
Basically.
The most used.
The most used are resolution four.
And three. You want to avoid.
You will want to.
To avoid resolution three.
Because you cannot estimate the impact.
But the logic is that.
If you want to have a resolution five.
You might just as well.
Execute the.
The whole factorial.
But.
That's basically it.
The.
The alias.
Is the main.
Basically the main.
The main component behind the.
Behind the functional factorial.
So.
Let's see.
We would want to.
Run.
A resolution three design.
So we want to.
But run.
So we can.
And basically.
Jeff's gonna.
Tell us.
That.
The main effects.
They are always.
With the interact.
That's what.
It occurs when.
One.
Is.
What.
It occurs.
Certain facts are.
They are.
They are.
For each other.
So.
This is due to the nature.
We have.
We have five variables.
Only.
So.
As you can see.
Here.
Here.
And the color map.
The black.
They.
Fully correlated.
Variables.
So.
Basically.
What.
Zero.
You.
You have.
With this design.
Successfully.
Decorrelate.
This.
So you can.
The table.
Here.
You have.
Five factors.
But with only eight months.
So.
If we wanted to.
To study.
We could.
We.
All the factors here.
And basically you could do.
You could do it.
In eight months.
So.
You would have this result.
So.
Basically.
I think.
You guys.
Have situations.
Already.
Best situations where.
It was hard to.
I had to make.
Trade offs.
So that's where.
Professional.
Factorial.
The fraction of factorial.
As I.
It is a.
Screen.
Because.
That is.
To.
But.
It's.
Basically.
In the context of the.
This.
Which.
Variables.
Have the most significant.
So we could.
Here the fraction of factorial.
Design.
News.
With the resolution design.
But what if one of these.
Variables.
We saw that.
The pin position.
Have a lot of.
What we drop.
One of these.
So that we.
Create a better.
A better.
Design.
Greater resolution.
If we could drop.
One of these variables.
We.
Would have only.
Resolution.
For.
Or better.
Designs.
So when we create.
A resolution.
Even with.
Study for.
We.
Have a better estimate.
Of the problem.
To face.
So.
As you can see.
So.
You can estimate.
You can estimate.
You can estimate.
More.
More factually.
In fact.
So.
There are basically.
Two main types of screen designs.
There is the.
Classical design.
Basically.
And the main fact.
The classical screen design.
Is more suitable for scenarios.
Where.
The standard screen design.
These designs.
They include a fraction of the.
Designs.
And.
In the catapult experiment.
A fraction of the design.
Could be employed to efficiently.
Screen multiple controllable.
So we could remove.
A few variables.
And thus as I demonstrated.
Reducing the number of experimental.
Runs that require.
To start the experiment.
So basically.
The screening experiment.
It aims to.
To identify factors that.
Affect the response variable.
So let me.
Share this presentation.
So basically.
Basically.
The screen.
The screen designs.
Prioritize the.
The main effects.
Over the complex.
Interactions.
High order interactions.
They don't matter much.
In most of the systems.
So the focus.
Is more in main facts.
And standards.
First order and second order interactions.
So.
The primary goal.
Of the screen design.
Is to efficiently determine.
Which factors is going to influence.
The response variable.
And which of these.
Of these factors.
Do merit.
Merit for the investigation.
So.
We have two designs.
Which are.
Two designs.
This one that I just showed.
And we have also.
Four designs that are.
These are commonly.
To.
To study a lot of.
At the same time.
So.
So the.
The effect.
Hierarchy.
Hierarchy.
Sorry.
It's basically.
It dictates that.
Lower order.
They are much more likely.
To be important than higher order interactions.
So basically.
The main factor for our design.
And.
The application.
Is that.
Main factors for the designs.
They focus much more on.
Understanding.
The impact of primary effects.
On the response variable.
So basically the.
Features of the screen design.
Is underpinning.
By the principle of dispersion.
Effect dispersion.
Which causes.
Basically that.
Most variation.
In the response.
It can be explained by.
A small number of.
Effects.
Basically that.
So.
It would be good for us to.
Try to analyze.
The design.
And basically.
Yeah.
So how would we do this?
First. We.
Generated.
This design.
Screen of resolution.
And basically.
We should run.
The eight experiments.
With the catapult.
But this time.
Taking into consideration.
All the.
All the effects.
I encourage you guys to try.
And generate the design.
I encourage you guys to.
Choose different resolution designs.
So we can analyze.
The different effects.
That the resolution.
In trying to.
The resolution.
In.
On the design.
So maybe one of you.
Can use resolution three.
And other of you.
Can use resolution four.
Of course.
Increase the number.
Of runs you have to run.
Could be a little bit.
In my case here.
I'm running a resolution three design.
That's right.
Four factors.
We have one more.
Which is.
To complete the file.
And our goal here is to find.
Any of these factors.
And it's the lowest.
Resolution.
Calculation.
Resolution four.
Calculation.
The minimum.
By GPU.
Five.
Six.
Eight.
Seven.
It's interesting to see.
Because.
Such a simple.
Environment.
And even though.
It already.
Offers a pretty tedious.
And time consuming.
Process of.
Gathering data.
So.
Imagine a more complex.
Environment.
Or factory or laboratory.
Where you really want to.
Control.
The set of conditions.
Sometimes it's hard.
Sometimes it's impossible.
Especially when you have.
The human element.
I don't know.
About you.
What kind of conditions you guys.
Are facing.
In your research labs.
But.
The more you can.
You are able to control the environment.
The easier it is.
The data gathering process.
Is really the.
The worst part.
The most.
Troublesome.
Huge factor.
It's.
Interesting.
Because you guys are going to face.
Aero stricken here.
I don't know if you.
Already.
Already.
Hit the wall.
Here but there's a restriction.
In the experiment.
So there is a moment where.
The firing angle is.
At its maximum position.
And the release angle.
It cannot be.
At its lowest position.
This represents a restriction in the experiment.
So we cannot test.
How would be.
The firing angle.
At 140 degrees.
And the release angle.
At.
105.
Because it's just not.
It's not operational.
I faced.
Challenges like this.
In my application.
And in the light factory.
The light factory.
Problem.
You have to.
To revolve.
To revolve.
The.
Of.
I don't know.
If you really.
We really.
Have to.
Pay attention.
In the restriction of the experiment.
There is one factor that.
Interacts with each other.
Which is the.
And the.
Both of these factors.
They represent.
A construction.
A restriction.
In the.
Experiment.
Because you cannot set.
You cannot set.
Firing angle.
At its lowest.
And.
Release.
At the lowest.
At least.
So.
This experiment.
The.
The lowest value of.
Release angle.
Must be.
It must be.
Otherwise.
You.
To fit the table.
Unless.
The design.
You.
Random.
Do not.
Do not.
Cover.
This point.
Do you guys have any restrictions.
So far.
Any of you.
It's better for this.
It's going to have to be.
Not.
To see if we can.
Facilitate.
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on 2024-03-11