 Coordinators IIT Madras

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This course is addressed towards students, researchers and engineers carrying out experiments in their fields of study and work.  In depth knowledge of probability and statistics, though helpful, is not a pre-requisite to understand the contents of this course.  The first part of the course deals with random variables, typical probability distributions, random sampling, confidence intervals on population parameters and hypothesis testing.  These form the basic background of statistical analyses.
In the second part of this course, design of experiments and regression analysis are introduced.  The factorial design of experiments involving two or more factors is discussed in detail.  Properties of orthogonal designs and other popular design strategies such as the Central Composite Design and Box Behnken design are also discussed.  The characteristic features of experimental design strategies are defined and compared.
Linear regression model building concepts are explained using which empirical models may be fitted to experimental data.  The methods to assess the quality of the models fitted are discussed.
Identification of optimum performance of the process through experimental investigations is demonstrated through the response surface methodology approach.
After understanding this course material, the experimentalist will develop the confidence to identify an appropriate design strategy suited for his work.  He will also be able to interpret the results of the experiments in a scientific manner and communicate them unambiguously.

1. Random Variables
2. Introduction to discrete and continuous random variables, quantify spread and central tendencies of discrete and continuous random variables

3.  Important Statistical Distributions
4. Properties and applications of Normal, log-normal and t-distributions, Chi-Square and F distributions

5. Point and interval estimates of population parameters
6. Point Estimation of the population mean, distribution of the sample means, central Limit theorem, confidence Intervals on the population mean, optimal sample size to obtain precision and confidence in interval estimates of mean, maximum likelihood parameter estimation

7.  Hypothesis Testing
8. Formulation of null and alternate hypotheses, errors in hypothesis Tests, power of hypothesis tests, hypothesis tests on population means, variances and ratios of variances

9. Analyze single factor experiments
10. Introduction to Analysis of Variance (ANOVA), blocking and randomization

11.  Factorial Design of Experiments
12.  Need for planned experimentation, factorial design experiments involving two factors, effect of interactions, ANOVA in factorial design, general factorial design, partial factorial designs

13.    Linear Regression Analysis
14. Matrix approach to linear regression, Variance-Covariance matrix, ANOVA in regression analysis, quantifying regression fits of experimental data, Extra sum of squares approach, confidence intervals on regression coefficients, lack of fit analysis

15. Comparison of different experimental design strategies
16. Properties of orthogonal designs, implications of different factorial design models, importance of center runs, scaled prediction variance, central composite design, Box-Behnken design, moments of experimental designs, rotatable of experimental designs, face centered cuboidal designs, comparison of experimental designs

17. Response Surface Methodology
18. Method of steepest ascent, first and second order models, identification of optimal process conditions

Detailed Course Plan – Part 1

 Lecture No. Topic 1 Introduction and overview 2 Random Variables 3 Discrete Probability Distributions 4 Example Problems 5 Continuous Probability Distributions 6 Normal and Log Normal Probability Distributions 7 t-distribution 8 Chi-Square Distribution 9 F-distribution 10 Example Problems 11 Example Problems 12 Distribution of the random sample mean 13 Central Limit Theorem and its applications 14 Confidence Intervals 15 Maximum Likelihood Parameter Estimation 16 Example Problems 17 Formulation and Testing of Hypotheses 18 Errors in Hypothesis Testing 19 Hypothesis tests on population means, variances and ratio of variances 20 Example Problems

Detailed Course Plan – Part 2

 Lecture No. Topic 21 Design and Analysis of Single Factor Experiments 22 Randomized Block Design 23 Example Problems 24 Factorial Design with Two Factors 25 Factorial Design with Multiple Factors 26 Fractional Factorial Design 27 Example Problems 28 Matrix Approach to Linear Regression Analysis 29 Variance-Covariance Matrix 30 ANOVA in regression Analysis and Confidence Intervals 31 Extra Sum of Squares 32 Lack of Fit Analysis 33 Example Problems 34 Properties of Orthogonal Designs 35 Importance of Center Runs 36 Central Composite Design 37 Box Behnken Design and Face Centered Designs 38 Response Surface Methodology : Method of Steepest Ascent 39 Identification of optimal process conditions 40 Example Problems

Basic knowledge on Calculus, linear algebra and elementary knowledge on probability

• Montgomery, D. C., G.C. Runger, Applied Statistics and Probability for Engineers. 5th ed.New Delhi: Wiley-India, 2011.

1. Montgomery, D. C., Design and Analysis of Experiments. 8th ed.New Delhi: Wiley-India, 2011.
2. Myers, R. H., D. C. Montgomery and C. M. Anderson-Cook, Response Surface Methodology. 3rd ed. New Jersey: Wiley, 2009.
3. Ogunnaike, B. A., Random Phenomena. Florida: CRC Press, 2010.