[How To] Perform Design Of Experiments (DOE) using Minitab

Hiii all....!!!

Back with a typical post which is related to process optimization using software i.e., Minitab, simply performing Design of Experiments(DOE).

I've done final year project during BTech on 'Treatment of Industrial waste using Coaggulation - Flocculation with Minitab using DOE & Response Surface Methadology'. A special thanks to Mrs. Kalyani Gaddam & Mr. Shishir Kumar Behera for their guidance.

Most of you are having good knowledge on this topic, but recently i've received a request asking to demonstrate, as on we currently there is no related content which can be easily understandable by process engineers.

So i've taken initiation to explain it here.

To be a perfect engineer, one should be able to perform calculations manually as well as should be in a position to workout through software's. But most of the companies are not able to provide those to their engineers. But believe me, working with those will have an awesome feeling.

Also Read:

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[How To] Evaluate the required quantity of moisture adsorbents ?

Getting into the topic, Minitab is a package of many purposeful applications. Can draw graphs to evaluate the trends, can evaluate the moving ranges of the variables, can define some random equations based on the available data(regression), Can be used during process optimization stage of product manufacturing.

So, here i'm gonna provide you a small demo about optimization using minitab step-wise manner.

Let the case be particle size distribution, we have to get a desired PSD from a customized isolation step. In this case the variables / factors would be Cooling temperature, Agitator Speed, Rate of cooling. And the output will be d(0.1), d(0.5), d(0.9) with some desired specification.

Let the raw limits of the variables / factors would be 

Cooling temperature : 0 - 20 °C,
Agitator RPM             : 20 - 60,
Rate of cooling           : 10 °C / hour.

Let the expected response be d(0.1) = 10 - 50 µ, d(0.5) = 50 - 100 µ, d(0.9) = 100 - 200 µ 
& yield % = 80 - 90%.

Lets start the show,

Step - 1: Open Minitab, [I'm using Minitab 18].

Step - 2: Click on STAT in main menu bar and then enter the DOE from the drop down,

Also Read:

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Select Screening > Create Screening design.
Below screen will appear.

Select Definitive screening.

Step - 3: Set number of factors to 3 (As our output PSD will depend on cooling rate, agitation rate & Cooling temperature, factors shall be 3).
For proceeding further click on designs and close that then the factors option will be highlighted.

Now click on Factors, it will look like below:

Enter the Low & High values as shown above in the factors dialogue box and click OK.
Again Click OK. random runs will be generated like shown below:

Step - 4: Random runs & experiments.





As like shown above, total of 13 random runs are generated and now experiments need to be performed in lab scale (preferably in laboratory Auto reactors replicating plant agitators). 

Also Read:

[How To] Perform a Material Balance ? 

[How To] Design a chilled water system ?

Step - 5: Responses 

After getting the results, we have to fill the results in C8, C9, C10 & C11 columns in the work sheet. Below are some of the tentative results.

Step - 6: Analyzing the response.
Click on Stat > DOE > Screening > Analyzing Screening Design.

By clicking the 'Analyse Screening Design', a window will appear like below shown:

Now we have to select the responses that we need to analyse, now i'll be selecting all the available four responses,

Then Click Ok.

Step - 7: Analyzing the Graphs (Pareto's).

As we have selected a total of 4 responses, 4 pareto graphs will appear on screen, below screenshot fyr:

Now you may get a doubt, 'what does these graphs represent and what we need to understand ?',
Actually in the before clicking Ok, we have to select % of confidence in 'Graphs' option.
Which means the graphs will show that what factors will impact the responses with 95% significance level.

Also Read:

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Let me explain you clearly,
First graph is Yield Vs Factors(Cooling time, Rate, RPM):

There will be a red coloured line over the graph, which represents the standard, the bars which are above the line are said to be having impact over yield. So in the first graph, Factor B, C are having impact on yield, Factor B, C are RPM & temperature, and the factor A is below the standard line, which indicates that Cooling rate(A) is not having considerable impact.

Similarly,
Second Graph ( d(0.1) Vs Factors ):

Factor C(Temperature) bar is below the standard line, hence it is not having impact on d(0.1), whereas factors A, B are above the reference line, hence both of then are having impact on d(0.1).

Third Graph ( d(0.5) Vs Factors ):

Factor B(RPM), C(Temperature) bars are below the standard line, hence it can be said that those two factors are not having significant impact on d(0.5) response, whereas factor A is having significant impact on d(0.5).

Fourth  Graph ( d(0.9) Vs Factors ):

Factor B(RPM), C(Temperature) bars are below the standard line, hence it can be said that those two factors are not having significant impact on d(0.9) response, whereas A is having significant impact on d(0.9)..

That's it, now half of the job is done. You understood the pareto's.

Step - 8: Finding the Regression equations.

If you close all the pareto's, there will be a Session / Activity sheet.
This sheet will record all the process that we have done.





Below is the screenshot fyr:

Now, lets expand each of them.

Yield % Vs Factors:

In the model summary, there will be R-Sq, here it is shown as 66.10%, which indicates that the model is not stable. For a stable model the R-Sq value should be greater than 90% [Some times the design experts will consider even 80% also as stable, but i'll consider 90% as stable].

Regression equation is 87.77 - 0.053 x Cooling rate - 0.2050 x RPM - 0.36 x Temperature.

Using this equation we can predict the yield %, once if the factors are known.

Similarly for other responses also, there will be the regression equations.

Step - 9: Optimizing the response.

This is what we need actually, finding out the optimum response based on our requirement. 
As we need the Yield % in 80 - 90%, d(0.1) : 10-50 µ, d(0.5): 50-100 µ, d(0.9): 100-200 µ.

Navigation to Response Optimizer:

Stat > DOE > Screening > Response Optimizer.

By clicking that, a window will appear as below:

As we have total of four responses, they will appear and we have to select the range for them.

Available options for them are Do Not Optimize, Minimize, Target, Maximize.

From these 4 we have to select any one for the responses.

As we need Yield % in range of 80-90%, i'll prefer it as 88% by selecting target option,
For d(0.1), i'll select 30 as target, 
For d(0.5), i'll select 80 as target,
For d(0.9), i'll select 150 as target.

Below screenshot fyr:

Then Click Ok.

The optimum value will appear for you. Below Screenshot FYR:

The optimum values are Cooling rate : 5 ℃/hr, RPM : 37.77, Temperature : 0 ℃.

Apart from this we have to check one more thing here, that is desirability which is denoted by d.





The desirability d represents the total probability. If its above 95% the optimized response is reproducible, or else not.

In our case the average desirability is 61.28%
Individual desirability are

Yield % : 58.81 %,
d(0.1)    : 67.79 %,
d(0.5)    : 93.95 %,
d(0.9)    : 37.65 %.

So from the above, we can say that the probability of reproducing the desired response is very less.

So if we change the targets to different values, the optimum values might vary and desirability might increase / decrease.





That's it.......!!!!!

Hope you understand, this is the basic explanation and i'll generate a video in future explaining this topic in detail.

Any queries feel free to comment. or reach me at pharmacalc823@gmail.com.

Comments are most appreciated......!!!!




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About The Author

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Hi! I am Ajay Kumar Kalva, Currently serving as the CEO of this site, a tech geek by passion, and a chemical process engineer by profession, i'm interested in writing articles regarding technology, hacking and pharma technology.
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