Hi. Hello, everyone.
This is Cheng Ting here,
and the other presenter today will be Cui Yue.
Today, we are going to share with you our experience
of exploring JMP DOE design
and the modeling functions to improve the sputtering process.
First of all,
let's have a brief background and introduction about the project.
This is the Black Belt Six Sigma DMAIC Project
regarding to the sputtering process.
The project goal were to optimize several film properties.
In the define phase, we have identified the three CTQ
and the three correlated success criteria.
CTQ 1 is the most important and a challenging one.
The success criteria
is the measurement result is larger than 0.5.
CTQ2 and CTQ3 are equally important.
The success criteria for both of them
is the measurable result should be less than 0.05.
Different JMP tools has been applied massively throughout the measure phase,
analyze phase, and improve phase.
We will share our experience of using the JMP tools here.
In the measure phase, we did a MSA, and we finalized the data collection
for the baseline hardware.
Three tuning knobs, namely X ₁, X ₂, and X₃ are involved.
After data collection,
we use a Monte-Carlo simulation in JMP to analyze the baseline capability.
This is the first tool we introduce today too.
In order to establish your baseline model,
we use augmented DOE, RSM, prediction profile,
as well as interaction profile, check functions in JMP.
After entering the analyze space,
in order to do a root- cause analysis and the capability analysis,
we use the goal plot,
desirability function, multivariate method,
and the graphic analysis tools.
In the improvement phase, we did hardware modification,
where another tuning node X₄ was introduced.
Interactive graph, augmented DOE,
RSM, desirability function, and interaction profile were used
in this section to further improve the process.
The GOSS stepwise fit and desirability function were used
in the robust DOE modeling to further improve the process.
Some of these tools will be demonstrated by Cui Yue later.
The control phase will not be covered at today's presentation.
As we mentioned, in the measure phase,
so after the baseline collection, we actually use the Monte-Carlo simulation
to understand the baseline process capability.
These are the baseline capabilities for three CTQs.
We can see that all of them are normal distribution,
indicating a strong linear correlation with the input parameters.
For CTQ1, the sample mean is out of spec limit.
Thus, we have a very negative Ppk value.
The 99 % of the baseline process result cannot meet CTQ1 spec at all.
CTQ2 is close to the spec among the three CTQS.
Sample mean is lower than the up spec limit.
Thus, we have a positive Ppk .
The 48 % of the baseline process result, they do not meet the spec for CTQ2.
Sample mean for the CTQ3 is out of spec limit as well.
Thus, it has negative Ppk.
64 % of the baseline process result did not meet the spec.
This baseline capability confirmed
that the biggest longevity for this project is C TQ1.
Apparently, the baseline process condition,
which we'll call process conditional 1 here,
cannot meet our CTQ success criteria, especially for CTQ1.
We will need to tune the process condition.
However, before that, we will need to know
if the current hardware can meet the requirement or not.
The subject matter experts, the SME, has advised us,
has proposed the two hypothesis, and advise us to shift the process
to condition 2 based on the second hypothesis.
However, before that, we will need to check
if the prediction model is good for both condition.
Hence, we use the scatter plot to check the collected data structure.
As we see here, the data collected is not in a orthogonal structure.
This is because we actually use a two- step evaluation design,
and widen the process range to meet the success criteria of CTQ1.
We did have a weak prediction capability in the whiter area.
However, we still have good prediction for the condition 1 and condition 2.
We also did a confounding analysis.
The fact there is certain confounding risk in the Resolution II between X ₁ and X₃.
Nonetheless, we still built a prediction model.
We use the response service method for the fitting.
In this case, the main effect, interactions,
and the quadratic terms will be fitting together.
Based on the RS, S R as well, RS- adjusted square, and the p value,
we can see it's a valid prediction model.
From the effect summary,
we can see that only the significant terms are included in the model.
With the interaction profile, we can see two interactions
which are correlated with two hypothesis we mentioned before.
With the prediction profile, we pick the process condition 2.
At this process condition,
what we can see here is 95 % of the confidence interval of CTQ1
is between the range of 0.5 and 0.6.
This CTQ has been tuned into spec.
However, in the meantime, the CTQ2 and the CTQ3 are out of stack.
Hence, we use the goal plot to compare the two process conditions,
and re alize that when we have improved CTQ 1
from process condition 1 to process condition 2
by getting closer to the target
and a narrowing down of standard deviation.
However, in the meantime, C TQ2 and 3 were compensated
with larger standard deviation and the further distance to the target.
Hence, there is a tradeoff between three CTQs.
In this case, we try to find an optimized solution
with the desirability function in JMP.
For CTQ1 , the success criteria is that mode of 0.5.
H ere, we use the maximum plateau method when set the desirability function.
Means any value more than or equal to the target
will be equally preferred.
We also highlight the importance of CTQ 1 by putting 1.5 as the important factor.
Fo r CTQ2 and 3, the success criteria is less than 0.05.
Hence, we use the minimum plateau when set the desirability.
Any value less than or equal to the target
will be equally preferred.
However, after maximize the desirability,
the calculated optimized solution is only around 0.02,
and none of the three CTQs can meet the success criteria.
Hence, we can conclude that there is a hardware limitation
in this case.
After discussion with the SME,
we decide to introduce Y₄ into our data analysis.
Y₄ is not a CTQ here,
but it is a measurement that can reflect the intrinsic property of the process.
This intrinsic property will affect the CTQ2 and CTQ3 directly.
if Y₄ is more than zero, then it's a positive process,
and when that Y₄ is less than zero, it's an active process.
If Y₄ is closer to zero, then we call is a neutral process,
which lead in to a smaller number of CTQ2 and CTQ3 together.
Here is the distribution of Y₄ of the baseline hardware.
As what we can see here with the baseline hardware,
the Y₄ is always more than zero.
That, we will always have for positive process.
The multi variate graph here actually shows the relationship
among the Y₄: CTQ2 and CTQ3.
They are strongly correlated.
If we have smaller Y₄, we will also have smaller CTQ2 and CTQ3.
In order to have a wider range of Y₄,
we decide to add in another factor, X₄, in the improve the hardware.
Together, another two scientific hypothesis
has been proposed by the SME.
We have collected data on the new hardware
and compare the Y₄ distribution in two hardwares.
In the baseline hardware, without X₄ , we have collected data orthogonally
and with certain range for each factor.
This is the distribution of the Y₄ under these contributions.
With the improved hardware, with the X ₄ introduced,
we have collected data in the same range of X ₁, X ₂, and X ₃.
This time, Y₄ a t different X ₄, has also been collected.
Comparing the two distributions, we can see that without X₄ ,
we only see one cluster for Y ₄, with the peak value more than zero.
However, with the X₄ introduced,
we can observe a bimodal distribution for Y₄,
with one peak with mean more than zero, and another peak with mean less than zero.
The process condition makes Y ₄ less than zero
actually draws our attention.
Under these process conditions, we will have negative process,
and this may help us to improve CTQ2 and CTQ3,
but choose that process if we cannot meet all CTQs in one process only,
because neural process benefits CTQ2 and CTQ3.
We did a simple screen of processed conditions
when we have a negative process, and this lead us to a certain range of X₄.
That's why we collect more dat a in this range,
because it's our condition of interests.
Now, we conclude that the X₄ did impact on Y ₄,
and thus, it can impact on CTQ2 and CTQ3.
Now, we can further with the impact of X₄ on CTQ1,
and build another model for the improved hardware.
Prior the data collection,
we have prescreened the conditions of interest
using the interactive graph in JMP.
We will collect more data with certain range of X₄,
because this X₄ actually can give us the negative Y₄ value.
It also covers most ranges of Y ₄.
As we can see here, before the data collection,
as what we can see here,
this is not the most orthogonal structure,
since we have collected more data at the conditions of interests,
even though after doing a design evaluation,
we find a low con founding risk.
The data structure is still good for modeling.
This is the model we constructed.
As what we can see here, we have an adequate model.
Only factor with the p value less than 0.05,
or what included in the model.
The RS quare is more than 0.8.
The difference between the R Square adjusted
and R Square is less than 10 %.
The p value for the whole model is always less than 0.0 01.
Also, through the interaction profile, the hypothesis 1 to 4 has been validated.
This time, can we find any optimized solution?
Again, we run the desirability function.
The left side is the optimized solution provided with the baseline hardware
before the X₄ installment,
and the right side is the optimized solution
with the improve d hardware with X₄ installments.
As what we can see here, compared with the baseline hardware,
improve d hardware did provide an optimized solution
with higher desirability and improve the result for each C TQ.
However, the desirability is still low, which is only 0.27.
Not all CTQs meet the success criteria in one step.
So we still did not find that adequate solution
in one-step process for the project.
However, but as what we mentioned previously,
since we have a cluster of the process conditions,
allow us two negative process with the Y ₄ less than zero.
We can propose a potential solution with two- step process.
The solution with two- step process may not be that straightforward.
As we know, if we can find the optimized solution in one step,
all we need to do is just to round the process at the conditions,
gives the maximized desirability.
The result will be predictable since we have a known model for it.
Now we want to have a two- step process.
For each step, we have a known model,
and if the process condition is determined.
However, due to the different process duration for each step,
we will have a new model for the final results.
In this new model, we will have nine variables in total:
X ₁ to X₄ for each step, and the duration for each step.
Now, the question is,
how are we going to find a proper solution for the two- step processes?
We've got two strategies.
The first one is to do a DSD modeling for the nine variables.
In this case, we will need to have at least 25 runs for the first trial.
Of course, we will have orthogonal data structure.
The RS M model can be constructed, but the cost will be very high.
The other strategy is to screen design
with the group orthogonal super-saturated design first,
which is the GOSS design.
In this case, we can screen the impact of seven variables with six run.
This is why it's super- saturated.
We have more variables than the data points.
Of course, we will need to screen out two variables
before the GOSS,
and we use the interactive graph again in this case,
and the details will be reviewed by the next slides.
The GOSS design provides
two independent blocks for each process step.
There is no interactions between the factors across block.
The data structure is orthogonal in each block,
making it possible to screen effect with the super-saturated data collection.
However, this GOSS will show the impact of main effect only,
and no interaction will be considered.
This is a low- cost approach, and we manage further DOE design.
The follow-up DOE can be DSD, augment, or OFAT.
Each of these has its own pros and cons,
and it will not be covered in this presentation.
Anyways, to save the cost, we decide to proceed with strategy 2.
We start with a GOSS design.
As we discuss ed now, we have nine different variables.
However, in the GOSS, we can only include seven variables.
In order to narrow down the parameters for the GOSS design,
we did a simple screen with the interactive graph.
For step 1, we choose the process conditions,
allow us to have a good CTQ2.
After screening,
we decide to fix X₂ in this case, based on the previous learning.
As seen here, when the CTQ1 is more than 0.5,
all we have is a positive process with the Y₄ for more than 20 %.
Hence in this case, for step 2, we choose process conditions,
allow us to have the Y ₄ less than -0.5 so we can have a negative process.
In this case, adding two steps together, the final Y ₄ will be closer to zero.
This way can improve in CTQ2 and CTQ3.
After screening, we decide to fix X₁ for this step,
based on the previous learning.
After data collection,
we did a step wise fit with main effect only,
since in the GOSS, as we mentioned previously,
only main effect is considered.
All three CTQs validated the model with the p value less than 0.05,
and the RS quare adjusted around 0.8, and VIF less than 5.
After maximize the desirability,
the model provide us with an optimized solution
with desirability more than 0.96, which is way higher than 0.27,
and not to mention 0.02.
Hence, we can actually lock the process parameters
and further by the optimized solution in next step,
which is we choose to use the OFAT.
But this will not be covered here.
Here, I like to summarize
what we have discussed in this presentation.
In this presentation, we have and share with you the experience.
We use different JMP tools involved in the data analysis
throughout the DMAIC project in different stages.
For the base line capability analysis, we have used Monte-Carlo simulation.
We also used a goal plot.
For the root- cause analysis, we used multivariate method.
We also used a graphic analysis.
In order to help with the DOE,
we used the augmented DOE, GOSS, and design diagnostic.
In terms to have a good model and prediction,
we used different fitting functions, and we also used the prediction profile.
We also used the interaction profile.
It also was mentioned that these profiles are not only used
for the model and the prediction,
but it also help us to have a deeper understanding
of the process itself.
In order to screen out the conditions of interest,
we actually use the interactive graph,
which is simple, but very useful and powerful.
In order to do d ecision making,
we actually use the desirability functions help us to make a decision.
Until now, we share with you our experience
of how the JMP can help us to do the analyze.
The last but not least,
we would like to thank Charles for his mentorship along the progress.
Thank you.
My partner Cui Yue,
she will share with you some demonstration with the JMP side.
She will help us to demonstrate
how can we use the interactive graphic analysis
as well the stepwise fitting in the GOSS model.
Okay, thank you.
Thank you, Cheng Ting.
I think you can see my screen now, right?
The first thing, I would like to introduce you
the interactive plot Cheng Ting has just mentioned.
This is actually one of my personal favorite function in JMP.
It's simple, but it's very powerful.
Here, our purpose is to screen what's the most relative function,
a factor relative to Y₄.
Which one contributes the most to Y₄, from X₁ to X ₄?
We can simply select all the factor of interest we want here,
and click OK.
Now, we are having the distribution of all the factors.
Now, as Cheng Ting has mentioned, we want to know what contributes the most
to the Y₄ at negative side.
For example, here.
Then now, we can see only X₄ from 13- 14, X₃ from 0- 1,
and X₂ at this range, 2.5 -5.
Also, X ₁ at 19-20, can make this happen.
Thus, it's easier to give us a range of different factors,
how it will contribute to Y₄, and how we're going to choose the factors
if we want the Y₄ reaches certain level.
Similarly, if we want it to be slightly higher than 0 %,
we can also simply click this area.
Actually, to be quite straightforward, to solve the problem at one shot,
we just select these two together.
Then, we can see, okay, X ₄ should be at this range,
maybe 10- 14.
X₃, definitely should concentrate at 0-1.
X₂ is a slightly wider distribution.
X ₁, there are o nly two c andidates for this direction.
From this one, we can easily and intuitively find
the contribution factors we want.
This is the first function I would like to demonstrate to you,
the distribution function.
There are many other things the distribution function can do,
including see the data distribution and test a lot of thing,
[inaudible 00:24:49] test , et cetera.
So I won't come in here.
The second thing I want to share with you is the GOSS.
It is actually the GOSS fit stepwise.
Now, we are having three CTQs.
All the CTQ, the analysis dialogue is open here.
For all the three, they have separate analysis dialogue.
To do a very straightforward way, we just the Control and click Go.
It will select the factors for all three C TQs at once.
Very straightforward.
These three will use the same stopping rule,
which is the minimum BI C.
Then, let's click Run M odel.
This fit model will give us our fitting separately for C TQ1, 2, 3.
Then, we need to modify the model or reduce the model one by one.
Here, our criteria is to choose the p value lower than 0. 05.
We define that value.
When the p value lower than 5 %, the factor is significant.
Here, we can remove X₄ .
Next one, for C TQ2...
For CTQ1, we are down here.
For CTQ2, we can remove X ₁ and X2 .
Okay, now we are having both lower than 0.05.
For X₃, w e also can do the same thing accordingly.
Let's move X₄ first .
All the three factors, p value are lower than 0.05.
We have get the reduced model.
Here at the bottom, we will have a prediction profiler.
If you don't have it, we can add it from the profiler function.
Then, we would like to find the optimum condition.
How we are going to do that?
We are going to use the desirability function.
First step, we will always be set the desirability,
which is already set here.
We have one me ta-gate to minimize.
Then, let's use the maximum desirability function.
H ere, we can find our optimum condition.
If we use Maximize and Remember, here is our optimal condition.
Then, we can use this condition to run the process
and valid ate the sequence again.
These are two functions I'd like to introduce you.
Okay, thank you.
Thank you.
