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Lesson 1: introduction to design of experiments, overview section  .

In this course we will pretty much cover the textbook - all of the concepts and designs included. I think we will have plenty of examples to look at and experience to draw from.

Please note: the main topics listed in the syllabus follow the chapters in the book.

A word of advice regarding the analyses. The prerequisite for this course is STAT 501 - Regression Methods and STAT 502 - Analysis of Variance . However, the focus of the course is on the design and not on the analysis. Thus, one can successfully complete this course without these prerequisites, with just STAT 500 - Applied Statistics for instance, but it will require much more work, and for the analysis less appreciation of the subtleties involved. You might say it is more conceptual than it is math oriented.

  Text Reference: Montgomery, D. C. (2019). Design and Analysis of Experiments , 10th Edition, John Wiley & Sons. ISBN 978-1-119-59340-9

What is the Scientific Method? Section  

Do you remember learning about this back in high school or junior high even? What were those steps again?

Decide what phenomenon you wish to investigate. Specify how you can manipulate the factor and hold all other conditions fixed, to insure that these extraneous conditions aren't influencing the response you plan to measure.

Then measure your chosen response variable at several (at least two) settings of the factor under study. If changing the factor causes the phenomenon to change, then you conclude that there is indeed a cause-and-effect relationship at work.

How many factors are involved when you do an experiment? Some say two - perhaps this is a comparative experiment? Perhaps there is a treatment group and a control group? If you have a treatment group and a control group then, in this case, you probably only have one factor with two levels.

How many of you have baked a cake? What are the factors involved to ensure a successful cake? Factors might include preheating the oven, baking time, ingredients, amount of moisture, baking temperature, etc.-- what else? You probably follow a recipe so there are many additional factors that control the ingredients - i.e., a mixture. In other words, someone did the experiment in advance! What parts of the recipe did they vary to make the recipe a success? Probably many factors, temperature and moisture, various ratios of ingredients, and presence or absence of many additives.  Now, should one keep all the factors involved in the experiment at a constant level and just vary one to see what would happen?  This is a strategy that works but is not very efficient.  This is one of the concepts that we will address in this course.

• understand the issues and principles of Design of Experiments (DOE),
• understand experimentation is a process,
• list the guidelines for designing experiments, and
• recognize the key historical figures in DOE.

Biostatistics and Design of experiments

--> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> -->

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

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Course layout, instructor bio.

Prof. Mukesh Doble

Course certificate.

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SWAYAM SUPPORT

Please choose the SWAYAM National Coordinator for support. * :

Shalabh [email protected] [email protected] Department of Mathematics & Statistics Indian Institute of Technology Kanpur , Kanpur - 208016 ( India )

MTH 513A : Analysis of Variance

Classes will begin on 5 January 2022 and continue in ONLINE MODE unless announced for offline or hybrid mode.

Course Contents: Analysis of completely randomized design, randomized block design, Latin squares design; Split plot, 2 n and 3 n factorials with total and partial confounding, two-way non-orthogonal experiment, BIBD, PBIBD; Analysis of covariance, missing plot techniques; First and second order response surface designs.

Online Course Platform: Course can be accessed through online platform MooKit available at https://hello.iitk.ac.in .

Expected topics to be covered: Likelihood ratio test for general linear hypothesis; Test of hypothesis for one and more than one linear parametric functions; Likelihood ratio test in in one way model; analysis of variance in one way model; multiple comparison tests; Analysis of completely randomized, randomized block and Latin squares designs; missing plot techniques;  General intrablock and interblock analysis of variance in Incomplete block designs; Balanced incomplete block design (BIBD); Intrablock analysis of variance in BIBD; Interblock analysis of variance in BIBD; Recovery of information in BIBD; Intrablock analysis of variance in partial balanced incomplete block design (PBIBD); 2 n factorial experiments with total confounding, partial confounding and fractional replications; Analysis of covariance; Introduction to 3 n factorials.

H. Scheffe: The Analysis of Variance, Wiley, 1961. H. Toutenburg and Shalabh: Statistical Analysis of Designed Experiments, Springer 2009.

D. C. Montagomery: Design & Analysis of Experiments, 5th Edition, Wiley 2001(Low price edition is available).

Who can explain better than himself who invented - Enjoy the book by Sir RA Fisher - The Design of Experiments Reference Books: D. D. Joshi: Linear Estimation and Design of Experiments, Wiley Eastern, 1987.

George Casella: Statistical Design, Springer, 2008. Max D. Morris: Design of Experiments- An Introduction Based on Linear Models, CRC Press, 2011. N. Giri: Analysis of Variance, South Asian Publishers, New Delhi 1986. H. Sahai and M.I. Ageel: The Analysis of Variance-Fixed, Random and Mixed Models, Springer, 2001. Aloke Dey: Incomplete Block Design, Hindustan Book Agency 2010.  

Grading scheme: Quiz: 30%,  Assignments: 30%  Mid semester examination: 20%,   End semester examination: 20%. 

Quiz conduct: Quizzes will be conducted through the MooKIT platform. If anyone has any internet issue, please inform. The pdf file of the quiz will be sent using appropriate mode. Preferable mode is the discussion forum on MooKit platform.

Class Schedule : Time table:  Tuesday: 8:00-8:50, Wednesday: 10-10:50, Thursday: 8:00-8:50, Friday: 8:00-8:50,

We will meet on zoom  every  Wednesday from 10:00-10:50 AM  (as of now)  over Zoom to discuss and tutorial.

Another session to meet will be announced  after the class depending upon the contents.

The zoom link will be forwarded through email. Better you install Zoom.

Announcements:

Classes will begin on 5 January 2022 and continue to hold in ONLINE MODE unless announced for offline or hybrid mode. First class will be on 5 January 22 at 10 AM.

1. The lecture notes and videos are prepared in detail assuming some students may not have studied statistics in B.Sc.

2. Details about quiz will be shared through email.

3 . All the students need to access the video lectures only from the MooKIT platform.

4. Relevant notes and slides are provided inside the MooKIT platform.

5. A Google upload link for the submission of all the assignments will be shared over email.

6. Assignments are to be done using only R software, wherever required.

7. The lecture slides in pdf format, lecture notes in pdf format and videos are available in MooKit.

8. The recordings of online classes will be uploaded on youtube link which will be shared after the class.

Note: The grading scheme may  change due to COVID-19 pandemic situation. It will be changed in consultation with the students.

C ontact hours: 24 X 7, by email, phone, what's app. (If possible and not so urgent, avoid calling between 12-9 AM.) Please  raise the course related queries inside the MooKit platform under "Forums" only.

Assignments

Assignment 1

Assignment 2

Assignment 3

Assignment 4

Assignment 5

Assignment 6  

Assignment 7  

Assignment 8

Note: Please submit the codes, commands, screenshot of output and interpretations along with the text output in a single file. The link for online submission of the assignments has been sent to the students through email.

                                  Feel in Class

Lecture notes for your help (If you find any typo, please let me know)

For the course MTH513 A, Lecture Notes 1 are only for the quick revision.

In other notes, try to follow only the content that is covered in the video lectures. The notes may have more contents for completeness.  The required notes are uploaded in the MooKit platform.

Lecture Notes 1 : Results on Linear Algebra, Matrix Theory and Distributions

Lecture Notes 2 : General Linear Hypothesis and Analysis of Variance

Lecture Notes 3 : Experimental Design Models

Lecture Notes 4 : Experimental Designs and Their Analysis

Lecture Notes 5 : Incomplete Block Designs

Lecture Notes 6  : Balanced Incomplete Block Design (BIBD)

Lecture Notes 7  : Partially Balanced Incomplete Block Design (PBIBD)

Lecture Notes 8  : Factorial Experiment

Lecture Notes 9  : Confounding

Lecture Notes 10  : Partial confounding

Lecture Notes 11  :  Fractional Replications

Lecture Notes 12  : Analysis of Covariance

The video lectures are also available at Swayam Prabha DTH Channel 16   YouTube (Click here) . 

Slides and Videos used in the lectures: 

Course Status :	Completed
Course Type :	Elective
Duration :	8 weeks
Category :
Credit Points :	2
Undergraduate/Postgraduate
Start Date :	22 Jan 2024
End Date :	15 Mar 2024
Enrollment Ends :	05 Feb 2024
Exam Registration Ends :	16 Feb 2024
Exam Date :	24 Mar 2024 IST

links	download links
		Factorial Experiments
		Factorial Experiments	Factorial Experiment
		Factorial Experiments	and 2 Factorial Experiment
		Factorial Experiments	Factorial Experiment
				38
			Factorial Experiment	39
			and 2 Factorial Experiments	40

Video Lectures :

The following video lectures were created to help the students during COVID-19 pandemic 2020. It was not possible to do editing after the first recording due to the lockdown. The videos may have some minor slips as they were recorded in a single shot without much preparation and editing. I request you to kindly ignore the slips. The videos have been uploaded on www.youtube.com .

Enormous thanks to Prof. Satyaki Roy , Media Technology Centre and Wonderful Persons over there for their support in creating the videos.

These videos were prepared for the 2020 MSc Statistics students at IIT Kanpur. The 2021  MSc Statistics students at IIT Kanpur are requested to follow from MooKit.

Lecture 1: YouTube Link :  Slides of Video Lecture 1 : Factorial Experiment 

Lecture 2: YouTube Link :  Slides of Video Lecture 2 :  Factorial Experiment

Lecture 3: YouTube Link :   Slides of Video Lecture 3 :  Factorial Experiment

Lecture 4: YouTube Link :   Slides of Video Lecture 4 :  Factorial Experiment

Lecture 5: YouTube Link :  Slides of Video Lecture 5 :  Factorial Experiment

Lecture 6: YouTube Link :  Slides of Video Lecture 6 : Confounding (Video recording has been done at home, without any editing etc. So please excuse for minor slips of the tongue)

Lecture 7: YouTube Link : Slides of Video Lecture 7-8 : Confounding   (Video recording has been done at home, without any editing etc. So please excuse for minor slips of the tongue)

Lecture 8: YouTube Link :   Slides of Video Lecture 7-8  : Confounding   (Video recording has been done at home, without any editing etc. So please excuse for minor slips of the tongue)

About the Students :

How Design of Experiment evolved - An interesting article from https://www.sciencehistory.org/distillations/ronald-fisher-a-bad-cup-of-tea-and-the-birth-of-modern-statistics

Ronald Fisher, a Bad Cup of Tea, and the Birth of Modern Statistics

At the time, the early 1920s, Fisher worked at an agricultural research station north of London. A short, slight mathematician with rounded spectacles, he'd been hired to help scientists there design better experiments, but he wasn't making much headway. The station's four o'clock tea breaks were a nice distraction.

One afternoon Fisher fixed a cup for an algae biologist named Muriel Bristol . He knew she took milk with tea, so he poured some milk into a cup and added the tea to it.

That's when the trouble started. Bristol refused the cup. "I won't drink that," she declared.

Fisher was taken aback. "Why?"

"Because you poured the milk into the cup first," she said. She explained that she never drank tea unless the milk went in second.

The milk-first/tea-first debate has been a bone of contention in England ever since tea arrived there in the mid-1600s. It might sound like the ultimate petty butter battle , but each side has its partisans, who get boiling mad if someone makes a cup the "wrong" way. One newspaper in London declared not long ago, "If anything is going to kick off another civil war in the U.K., it is probably going to be this."

As a man of science Fisher thought the debate was nonsense. Thermodynamically, mixing A with B was the same as mixing B with A, since the final temperature and relative proportions would be identical. "Surely," Fisher reasoned with Bristol, "the order doesn't matter."

"It does," she insisted. She even claimed she could taste the difference between tea brewed each way.

Fisher scoffed. "That's impossible."

This might have gone on for some time if a third person, chemist William Roach, hadn't piped up. Roach was actually in love with Bristol (he eventually married her) and no doubt wanted to defend her from Fisher. But as a scientist himself, Roach couldn't just declare she was right. He'd need evidence. So he came up with a plan .

"Let's run a test," he said. "We'll make some tea each way and see if she can taste which cup is which."

Bristol declared she was game. Fisher was also enthusiastic. But given his background designing experiments he wanted the test to be precise. He proposed making eight cups of tea, four milk-first and four tea-first. They'd present them to Bristol in random order and let her guess.

Bristol agreed to this, so Roach and Fisher disappeared to make the tea. A few minutes later they returned, by which point a small audience had gathered to watch.

The order in which the cups were presented is lost to history. But no one would ever forget the outcome of the experiment. Bristol sipped the first cup and smacked her lips. Then she made her judgment. Perhaps she said, "Tea first."

They handed her a second cup. She sipped again. "Milk first."

This happened six more times. Tea first, milk first, milk first again. By the eighth cup Fisher was goggle-eyed behind his spectacles. Bristol had gotten every single one correct.

It turns out adding tea to milk is not the same as adding milk to tea, for chemical reasons. No one knew it at the time, but the fats and proteins in milk-which are hydrophobic, or water hating-can curl up and form little globules when milk mixes with water. In particular, when you pour milk into boiling hot tea, the first drops of milk that splash down get divided and isolated.

Surrounded by hot liquid, these isolated globules get scalded, and the whey proteins inside them-which unravel at around 160 degree Faherniet -change shape and acquire a burnt-caramel flavor. (Ultra-high-temperature pasteurized milk, which is common in Europe, tastes funny to many Americans for a similar reason.) In contrast, pouring tea into milk prevents the isolation of globules, which minimizes scalding and the production of off-flavors.

As for whether milk-first or tea-first tastes better, that depends on your palate. But Bristol's perception was correct. The chemistry of whey dictates that each one tastes distinct.

Bristol's triumph was a bit humiliating for Fisher-who had been proven wrong in the most public way possible. But the important part of the experiment is what happened next. Perhaps a little petulant, Fisher wondered whether Bristol had simply gotten lucky and guessed correctly all eight times. He worked out the math for this possibility and realized the odds were 1 in 70. So she probably could taste the difference.

But even then he couldn't stop thinking about the experiment. What if she'd gotten just one cup wrong out of eight? He reran the numbers and found the odds of her guessing "only" seven cups correctly dropped from 1 in 70 to around 1 in 4. In other words, accurately identifying seven of eight cups meant she could probably taste the difference, but he'd be much less confident in her ability-and he could quantify exactly how much less confident.

Furthermore, that lack of confidence told Fisher something: the sample size was too small. So he began running more numbers and found that 12 cups of tea, with 6 poured each way, would have been a better trial. An individual cup would carry less weight, so one data point wouldn't skew things so much. Other variations of the experiment occurred to him as well (for example, using random numbers of tea-first and milk-first cups), and he explored these possibilities over the next few months.

Now this might all sound like a waste of time. After all, Fisher's boss wasn't paying him to dink around in the tearoom. But the more Fisher thought about it, the more the tea test seemed pertinent. In the early 1920s there was no standard way to conduct scientific experiments: controls were rare, and most scientists analyzed data crudely. Fisher had been hired to design better experiments, and he realized the tea test pointed the way. However frivolous it seemed, its simplicity clarified his thinking and allowed him to isolate the key points of good experimental design and good statistical analysis. He could then apply what he'd learned in this simple case to messy real-world examples-say, isolating the effects of fertilizer on crop production.

Fisher published the fruit of his research in two seminal books, Statistical Methods for Research Workers and The Design of Experiments . The latter introduced several fundamental ideas, including the null hypothesis and statistical significance, that scientists worldwide still use today. And the first example Fisher used in his book-to set the tone for everything that followed-was Muriel Bristol's tea test.

His intellectual acumen, however, did not insulate Fisher from the prejudices of his time when it came to class, race, and colonialism. Fisher was a well-known eugenicist and was steadfast in those beliefs throughout his life. When, in the aftermath of World War II, UNESCO formed a coalition of scientists to wrestle with Nazi science and provide the scientific backbone for the universal condemnation of racism, Fisher was among those who officially objected to what he saw as the project's "well-intentioned" but misguided mission, affirming his belief that groups differed " in their innate capacity for intellectual and emotional development ."

Optimal design of gyroid solid-TPMS structures for 8-inch wafer prober lower chuck in additive manufacturing

• Original Article
• Published: 05 September 2024

Cite this article

• Kunwoo Kim 1 ,
• Sohyun Park 1 ,
• Seungyeop Lee 1 ,
• Siyeon Gu 1 ,
• Hyungug Jung 2 &
• Jaewook Lee 3  

The advantage of 3D printing is that it can create creative shapes that cannot be manufactured through existing subtractive manufacturing. It can also produce products with improved functionality. In this study, a radial structure with TPMS is applied to improve the temperature uniformity of the wafer prober lower chuck used in semiconductor inspection equipment. The gyroid solid-TPMS structure, the most basic of TPMS structures, is considered, and a 1/9 analysis model is constructed considering that it is an axis-symmetric structure, and optimization is performed through thermal flow analysis. Based on the proposed design, it was confirmed that when the optimization result offset was +0.57 mm, the temperature standard deviation was 0.01 °C and the pressure was 0.40 bar. Specimens were manufactured using the proposed optimal design, and the optimization results were verified through lab-based experiment.

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Acknowledgments

This research was supported by the Korea Institute of Industrial Technology (Project Number: JB240003).

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Daegyung Technology Application Division, Korea Institute of Industrial Technology, Daegu, Korea

Kunwoo Kim, Sohyun Park, Seungyeop Lee & Siyeon Gu

Staco Co., Ltd., Ansan, Korea

Hyungug Jung

Department of Smart Mobility Engineering, Kyungpook National University, Daegu, Korea

Jaewook Lee

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Corresponding author

Correspondence to Jaewook Lee .

Additional information

Kunwoo Kim received his B.S. degree from Pusan National University (2007), M.S. from Pusan National University (2009) and Ph.D. from Pusan National University (2014). And he is currently a Principal Researcher in Korea institute of industrial technology. His major area is a flexible multi-body dynamics, a nonlinear dynamics and design for additive manufacturing based on PBF and DED.

Jaewook Lee is an Assistant Professor of Department of Smart Mobility Engineering at Kyungpook National University (KNU). His research interest is a generative design for additive manufacturing sim-ulation of additive process based on laser powder bed fusion.

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Kim, K., Park, S., Lee, S. et al. Optimal design of gyroid solid-TPMS structures for 8-inch wafer prober lower chuck in additive manufacturing. J Mech Sci Technol (2024). https://doi.org/10.1007/s12206-024-2410-0

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Received : 29 April 2024

Revised : 20 June 2024

Accepted : 20 June 2024

Published : 05 September 2024

DOI : https://doi.org/10.1007/s12206-024-2410-0

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