DOE with 2 factors (3,4 levels) and optimized factor

L

lekerz

Dear all
Firstly I want to say that i am a new Minitab user and don't have any strong background in statistic. However, I want to use Minitab to determine the optimized reaction condition. The reaction relates with the two dominant factors (mixing times (4 levels) and agitator speeds (3 levels)). The reaction is monitored by measuring the change of SG (Response), which is targeted at 0.8067.
Does anyone could kindly help me step by step? I did try on ANOVA-GLM, but the result is shown as follows:

General Linear Model: SG versus Speed, Mixing Time

Factor Type Levels Values
Speed fixed 3 250 rpm, 400 rpm, 550 rpm
Mixing Time fixed 4 5 min, 10 min, 15 min, 20 min


Analysis of Variance for SG, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P
Speed 2 0.0000073 0.0000073 0.0000037 **
Mixing Time 3 0.0000006 0.0000006 0.0000002 **
Speed*Mixing Time 6 0.0000001 0.0000001 0.0000000 **
Error 0 * * *
Total 11 0.0000080

** Denominator of F-test is zero
.

Also I couldn't optimized the condition by using response optimizer function? Please advice me the solutions.

Wish your day is a blessed one:thanx:
Thank you so much..
Lekerz
 

Attachments

  • Reaction-Speed and Mixing Time.xls
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Miner

Forum Moderator
Leader
Admin
You have a fully saturated model. You either need to run a replicate in order to test the interaction, or take the interaction out of the model. This will free a degree a freedom to perform the F-test.

You can also analyze this as a General Full Factorial instead of GLM.

Minitab will only run response optimizer for 2-level factorials or response surface designs. It will not run for General Full factorials or GLM. You have to interpret the Main Effect Plots and Interaction Plots to optimize.
 
N

NumberCruncher

HI Lekerz

I will go one stage further than Miner. If possible, you really should perform a set of replicate experiments to determine experimental error.

Clearly, part of that decision will be judging the cost and time of carrying out the experiments vs the cost of a wrong decision. If these are the results of experiments on an entire production plant, I can understand why you may not want to do this again.

However, if these are laboratory based experiments, I think a repeat would be worthwhile.

To quote Yogi Berra, "You can see a lot just by looking".

Looking at the data, there is a clear trend of greater mixing time ---> greater SG (specific gravity?)

However, the response to mixing speed is U shaped. 400 rpm gives a lower SG than the two other speeds. Does this seem right to you? Is there a physical reason why this could be true? Personally, I have absolutely no idea whether this is a real effect or just an artefact of experimental error.

If you do have a U shaped response surface, optimisation is going to be a bit awkward since you can easily have two different combinations of speed and time which give the same response. I don't know how Minitab would handle that one.

You should perform your experiments at least one more time. If you get the same pattern of results, you can be more confident that any conclusions you make based on this data are less likely to be wrong.

If you get a different pattern of results, you need to look at how you are performing the experiments. Are the experiments being randomised for example?

NC
 
L

lekerz

Thank you so much Miner and NC

Actually, the experiment came from the product plant. Let me explain you more clear about the story. My manager asks me to validate/verify the agitator speeds and mixing times which relate to batch sizes of the fragrance products (that also have different formula--therefore they also have different Specific gravity--Please see the attached file for the detail). So, for each product, I design my experiments for three factors as follows
1.batch sizes-3 levels (small, medium, and large),
2.agiatator speed 3-levels (250 rpm, 400, rpm, and 550 rpm)
3. Mixing time-4 levels (5, 10, 15, 20 min)

So, in the experiment I posted, I would like investigate the effect of speed and time by fixing the batch size for the product "L" fragrance.

Thus far, my question is do i really need to do the experiment for all fragrance product? If so, it is really so much work to do. Are there any assumption that i can used to claim that "only one study can be used for all" For example, at medium batch size for all fragrance product, we should use the agitator speed at 400 rpm with the 15 minute of mixing time.
(By considering the SG for all fragrance product, there are not much significant difference)

Do you guys have any wise idea to help me figure out this problem?
For more information, in practical production, it is really hard to collect data as i designed because it mostly depends on the order from customer.:thanx:

Any suggestion is very valuable for me--Thank so much
Lekerz
 

Attachments

  • SG of Fragrance Product.xls
    13.5 KB · Views: 108
N

NumberCruncher

Hi Lekerz

I'm afraid you have a classic problem. This is less about statistics and more about economics.

I think the most practical suggestion I can make is to go with what seems best from your current data.

However, whenever you make a new batch of material, try a new set of condtions from your experimental set and get your replicates that way. Over time, you will hopefully build up a reliable set of data and base your production on that.

Not the answer you are looking for, but less disruptive and safer than making lots of assumptions about all batch sizes, all mixes, all days for the whole plant.

NC
 
L

lekerz

Hello NC
Thank you so much for your suggestion. I really appreciate for your help. However, so bad, the auditor needs me to conclude the relation to set the standard in Working Instruction in next few months. (It is impossible to collect all data i need due to many factors as i described in my previous post)
By the way, wish you have a great morning.
lekerz
 
A

Allattar

Well the factors will be identified in Minitab as text from what I can see in the Excel worksheet. It may be better to use them as numeric.

A couple of clever commands for this is to use the calculator and the function
WORD(Column, 1)
where 1 implies taking word 1 from the text string, and then use text to numeric to convert them to numbers.

In terms of the Sum of squares its difficult to see as the differences are quite small. But the Speed*Mix Time interaction is small compared Speed.

You could remove the Speed * Mix Time interaction and this would be used as the Error term.

The plotting suggestion is probably the best thing to do.
Use a scatterplot of SG v speed, you can also group by Mix Time.
A second scatterplot of SG v mix , grouped by speed is also interesting.

A 3d Scatterplot can work, but they can be a bit confusing to understand.

It looks like their is a quadratic in speed, the results dip at 400. There could be a linear relationship between mix time and SG, but the slope isnt very large.

You could define this as a custom Response Surface design, or use General regression. But only if you have got the values as numeric values.

Using a General regression of Spd, Mix T, Spd*Mix T and Spd*Spd I get.

Term Coef SE Coef T P
Constant 0.818053 0.0005855 1397.26 0.000
Spd -0.000059 0.0000029 -20.84 0.000
Mix T 0.000031 0.0000223 1.37 0.212
Spd*Mix T 0.000000 0.0000001 0.37 0.719
Spd*Spd 0.000000 0.0000000 21.13 0.000


Because we are using these as numeric values we can fit slopes, and rather than Number of levels-1 DF, we have 1 DF per term.

Reducing the model with the removal of the spd*Mix T interaction gives

Analysis of Variance

Source DF Seq SS Adj SS Adj MS F P
Regression 3 0.0000079 0.0000079 0.0000026 183.378 0.0000001
Spd 1 0.0000002 0.0000073 0.0000073 510.220 0.0000000
Mix T 1 0.0000006 0.0000006 0.0000006 39.230 0.0002422
Spd*Spd 1 0.0000072 0.0000072 0.0000072 500.321 0.0000000
Error 8 0.0000001 0.0000001 0.0000000
Total 11 0.0000080


Thats what I have come up with just on the analysis alone.

The SS values seems small but then the differences that we are looking at in the data are down to the 0.0001 level. What are you measuring?
 
L

lekerz

Well the factors will be identified in Minitab as text from what I can see in the Excel worksheet. It may be better to use them as numeric.

A couple of clever commands for this is to use the calculator and the function
WORD(Column, 1)
where 1 implies taking word 1 from the text string, and then use text to numeric to convert them to numbers.

In terms of the Sum of squares its difficult to see as the differences are quite small. But the Speed*Mix Time interaction is small compared Speed.

You could remove the Speed * Mix Time interaction and this would be used as the Error term.

The plotting suggestion is probably the best thing to do.
Use a scatterplot of SG v speed, you can also group by Mix Time.
A second scatterplot of SG v mix , grouped by speed is also interesting.

A 3d Scatterplot can work, but they can be a bit confusing to understand.

It looks like their is a quadratic in speed, the results dip at 400. There could be a linear relationship between mix time and SG, but the slope isnt very large.

You could define this as a custom Response Surface design, or use General regression. But only if you have got the values as numeric values.

Using a General regression of Spd, Mix T, Spd*Mix T and Spd*Spd I get.

Term Coef SE Coef T P
Constant 0.818053 0.0005855 1397.26 0.000
Spd -0.000059 0.0000029 -20.84 0.000
Mix T 0.000031 0.0000223 1.37 0.212
Spd*Mix T 0.000000 0.0000001 0.37 0.719
Spd*Spd 0.000000 0.0000000 21.13 0.000


Because we are using these as numeric values we can fit slopes, and rather than Number of levels-1 DF, we have 1 DF per term.

Reducing the model with the removal of the spd*Mix T interaction gives

Analysis of Variance

Source DF Seq SS Adj SS Adj MS F P
Regression 3 0.0000079 0.0000079 0.0000026 183.378 0.0000001
Spd 1 0.0000002 0.0000073 0.0000073 510.220 0.0000000
Mix T 1 0.0000006 0.0000006 0.0000006 39.230 0.0002422
Spd*Spd 1 0.0000072 0.0000072 0.0000072 500.321 0.0000000
Error 8 0.0000001 0.0000001 0.0000000
Total 11 0.0000080


Thats what I have come up with just on the analysis alone.

The SS values seems small but then the differences that we are looking at in the data are down to the 0.0001 level. What are you measuring?
Hi Allattar,
Firstly, thanks so much for your help and very informative answer. However, as I am a new minitab user and also weak background on statistics. If I don't bother you too much, could you please explain me step by step how to use the calculator and function to convert number to text, vise versa.--Also, do you have any recommend book for minitab dummy, like me?
Actually, my propose for this design experiment is to obtain the optimized and suitable conditions for the reaction.
 
L

lekerz

Dear All minitab Experts,
Could you guys help to review my result obtained from the Response Surface? Also, is it applicable? I have designed the experiment to obtain the optimized condition for the production of fragrance in the production line. The result obtained from the response optimizer is @ Agitator speed 315 rpm with the mixing time of 5 minutes. Is it correct and applicable?
(I don’t really know how to judge whether the result or model is correct or not, which parameters we must consider, R-square??—I am a minitab beginner and so really dumb in statistics; however I will try hard to ace on it)
Thanks:thanx:
Lekerz

Response Surface Regression: SG versus Speed (rpm), Mixing Time (min)
The analysis was done using coded units.
Estimated Regression Coefficients for SG
Term Coef SE Coef T P
Constant 0.806488 0.000072 11182.398 0.000
Speed (rpm) -0.000137 0.000041 -3.325 0.016
Mixing Time (min) 0.000290 0.000045 6.402 0.001
Speed (rpm)*Speed (rpm) 0.001638 0.000072 22.862 0.000
Mixing Time (min)*Mixing Time (min) -0.000113 0.000076 -1.481 0.189
Speed (rpm)*Mixing Time (min) 0.000023 0.000055 0.406 0.699
S = 0.0001170 R-Sq = 99.0% R-Sq(adj) = 98.1%

Analysis of Variance for SG
Source DF Seq SS Adj SS Adj MS F P
Regression 5 0.000008 0.000008 0.000002 115.41 0.000
Linear 2 0.000001 0.000001 0.000000 26.02 0.001
Square 2 0.000007 0.000007 0.000004 262.43 0.000
Interaction 1 0.000000 0.000000 0.000000 0.16 0.699
Residual Error 6 0.000000 0.000000 0.000000
Total 11 0.000008



Estimated Regression Coefficients for SG using data in uncoded units
Term Coef
Constant 0.817803
Speed (rpm) -5.93889E-05
Mixing Time (min) 8.06667E-05
Speed (rpm)*Speed (rpm) 7.27778E-08
Mixing Time (min)*Mixing Time (min) -2.00000E-06
Speed (rpm)*Mixing Time (min) 2.00000E-08

Response Optimization
Parameters
Goal Lower Target Upper Weight Import
SG Target 0.8017 0.8067 0.8117 1 1
Global Solution
Speed (rpm) = 315.180
Mixing Time = 5.014
Predicted Responses
SG = 0.8067, desirability = 1.00000
Composite Desirability = 1.00000

Surface Plot of SG vs Mixing Time (min), Speed (rpm)

Contour Plot of SG vs Mixing Time (min), Speed (rpm)


 

Miner

Forum Moderator
Leader
Admin
Rerun your analysis removing the following terms, which are not significant, then repost the results.

Mixing Time (min)*Mixing Time (min)
Speed (rpm)*Mixing Time (min)
 
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