Unit 1: General linear model: definition, assumptions, concept of estimability, least squares

estimation, BLUE, estimation space, error space, Guass Markov theorem, variances and

covariances of BLUEs, Tests of hypotheses in general linear models. Simultaneous testing of

general linear hypotheses: Bonferroni, Tukey’s , Scheffé’s tests, Fisher least significant

difference method; applications to CRD and RBD .

(12L + 3T)

Unit 2: Concepts of factorial designs, main effects, and interaction effects; Two-factor

factorial design and its analysis using fixed effect model; General factorial design; Analysis

of replicated and unreplicated 2k full factorial designs; Blocking and confounding in a 2k

factorial design; Construction and analysis of 2k-p fractional factorial designs and their alias

structures; Design resolution, resolution III, IV, and V designs; fold over designs; saturated

designs.

(12L + 3T)

Unit 3: The 3k full factorial design and its analysis using fixed effect model; Confounding in

3k factorial designs; Construction and analysis of 3k-p fractional factorial designs and their

alias structures; Factorials with mixed levels: factors at two and three levels, factors at two

and four levels; Design optimality criteria; Concept of random effects and mixed effects

models, analysis of 2k factorial designs using the random effect model, analysis of 2k factorial

designs using the mixed effect model, rules for expected mean squares, approximate F-tests.

(12L + 3T)

Unit 4: Response surface methodology: the method of steepest ascent, analysis of the

response surface, characterizing the response surface, ridge systems, multiple responses,

designs for fitting response surfaces; Robust parameter design: crossed array designs and

their analyses, combined array designs and the response model approach.

(12L + 3T)

References

1. Montgomery D.C. (2017): Design and Analysis of Experiments, 9th edition, John Wiley

& Sons, Inc.

2. Phadke, M. S.(1989). Quality Engineering using Robust Design, Prentice-Hall.

3. Voss, D., Dean, A., and Dean, A.(1999). Design and Analysis of Experiments, Springer

verlag Gmbh.

4. Wu, C. F., Hamada M. S.(2000). Experiments : Planning, Analysis and Parameter

Design Optimization, 2nd edition, John Wiley & Sons

- Teacher: S.B. Mahadik