Design and Analysis of Experiement



The objective of this course is to impart students at the PhD level with a holistic view of the fundamentals of experimental designs, analysis tools and techniques, interpretation and applications. Upon completion of this course, the students will know (i)basic statistics including ANOVA and regression, (ii)experimental designs such as RCBD, BIBD, Latin Square, factorial and fractional factorial designs , (iii)application of statistical models in analysing experimental data , (iv) RSM to optimize response of interest from an experiment,and (v) robust design of process and product.
Class lectures: 3 hours per week
Instructor:

img

Prof. J.Maiti,
Department of Industrial & Systems Engineering

Teaching Assistants:

img

Souvik Das

img

Sinjana Choudhuri



Prerequisites: Probability & statistics , basic knowledge in programming
Text & reference books:
Primary textbook: Design and Analysis of Experiments by D C Montgomery, Wiley.
Reference books: Applied Statistics and Probability for Engineers by D C Montgomery and G C Runger, Wiley. Design of Experiments-An Introduction Based on Linear Models by M D Morris, CRC Press.


Grading:

Final grades will be assessed based on three components:(i) internal assessment (IA) consisting of home assignments, term projects and attendance (20%), mid-term examination (30%), and end - term examination (50%).(ii) It is mandatory to submit home assignments (HA) and term projects (TP) within due dates. Failing of which leads to non - evaluation of mid - term or end-term answer scripts.(iii) Late submission will lead to reduction of marks in IA. If the assignment marks (e.g.,HA or TP) is x, the marks to be awarded will be x-d, where d is the delay in number of days. Zero marks will be awarded for d >= x

Home assignments & term project:

HW1:Basics of experimental design

HW2:Basic statistics

HW3:ANOVA

HW4:Regression

HW5:Experiments with blocking

HW6:Full factorial designs

HW7:Two level factorial designs

HW8:Blocking & confounding in two - level factorials

HW9:Fractional factorial designs

HW10:Response surface methodology


Course outline

 

Topics (with tutorials) Topics (with tutorials) Duration (Total=40 hrs.) 
 Module 1 Statistics  (i) Basic statistics ( 2 h our s ) (ii) ANOVA ( 4 hours) (iii) Regression ( 3 hours)  9 hours
 Module 2 Experimental designs  (i) RCBD ( 2 h our s ) (ii) Latin square  ( 2 h ours) (iii) BIBD  ( 2 h ours) (iv) CCD ( 2 hour)  8 hours
 Module 3 Factorial designs  (i) Full factorial designs ( 4 hour s ) (ii) 2 k factorial designs  ( 3 hours) (iii) Blocking and confounding in 2 k factorial  designs (2 hours) (iv) 2 k - p factorial designs (4 hours)  13 h ours
 Module 4 Response surface  methodology  (i) Method of steepest ascent ( 2 hours) (ii) Analysis of second order responses  ( 2 h ours) (iii) Multiple responses ( 2 h ours)  6 hours
 Module 5 Robust design  (i) Crossed array design (2 h our) (ii) Combined array design  (2 hours)  4 hours
 Module  6 Capstone  p rojec  All students require deciding a term project in a group of 5 students  together  just  after  completion of Module  1  

 

Instructions  for Tutorials , assignment &  term project :

 

(i) The  tutorials and  assignment will  have  to  be  programmed  by  the  students  either  in  R - studio or  in  SAS .  (ii) The   data  &   instructions  for   the   tutorials and  assignment shall   be   provided  be forehand. The tutorial class might also be converted to home assignments. (iii) The  problem  statement  &  data  sets  of  the  capstone  project  have  to  be  given  by  the  students by the end of  first module. The project should comprise of the applications  of the  DOE taught  throughout the semester in the  area of  quality or service .

 



    The full material of the course is given in the web page with the following link:


    Link: NPTEL, IIT Kharagpur



Home Assignment 1

  1. What is an experiment? Explain with an example.

  2. What is process model? Explain with an example.

  3. Define controllable and uncontrollable factors with example.

  4. What are the objectives of experiment design?

  5. Consider a case of your expertise/domain. Identify response variable of interest, controllable and uncontrollable factors. Develop a process model.

  6. What are the characteristics of a well-planned experiment?

  7. What are the steps involved in experimentation?

  8. What are basic principles of experimental design? What purposes they serve? Explain the principles with reference to the case you have developed (see question no. 5).

  9. Define treatment, treatment levels, treatment combinations and experimental settings. Explain with reference to the case you have developed (see question no. 5).

  10. What are the differences between replication and repeated measures?

  11. Define fixed effect and random effect models.

  12. What is blocking with respect to experimental design? Give one example. Why Blocking is necessary?

  13. What is confounding? When does it occur in experimental design?

  14. Explain with example one-factor complete randomized design (CRD).

  15. Explain with example one-factor randomized complete block design (RCBD).

  16. Explain with example two-factor complete randomized design.

  17. Explain with example two-factor randomized complete block design (RCBD).

  18. What is general factorial design? Explain with an example.

  19. What is 2K factorial design? When it is needed? What purpose does it serve?

  20. What is 2K-p fractional factorial design? Give one example? What are the advantage and disadvantage of fractional factorial design?

  21. Define the following experimental design:

    1. Factorial design with center point

    2. Factorial design with central and axial points

  22. What is robust design? Explain with an example.

  23. Comment on the orthogonality issues in experimental design.



Quick Links