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