Detailed Syllabus for Two-year M.sc. Course
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PART II 
  •  Paper - VA : Statistical Inference II  
Nonparametric Methods (20)
U-statistics and their Asymptotic properties. Nonparametric tests: Single sample location, location-cum-symmetry, and goodness-of-fit problems. Two-sample location, scale and homogeneity problems, Multisample location problem. Friedman Two-way Analysis of variance problem. Bivariate association problem, Cochran Q-test for dependent samples. Related Nonparametric Interval Estimation, Concept of Asymptotic Relative Efficiency. (20)
 
Decision Theory (15)
Decision problem and two-person game. Nonrandomized and randomized rules. Risk function. Admissibility of decision rules. Complete, essentially complete, minimal complete and minimal essentially complete classes. Essential Completeness and completeness of class of rules based on a sufficient statistic and the class of nonrandomized rules for convex loss. (6)
Bayes rules. Extended Bayes, Generalized Bayes and Limit of Bayes rules. Admissibility of Bayes Rules. (5)
Minimax rules. Method for finding minimax rules. (4)
 
Resampling Techniques (15)
Introduction to Jackknife and Bootstrap-methods for estimating bias, standard error and distribution function based on iid random variables. Standard examples. (8)
Consistency of the Jackknife estimate of the variance in the iid set up.Jackknife and Bootstrap estimates of regression parameters and the error variance. (3)
Bootstrap confidence intervals. (2)
Computational Aspects. (2)

References :
J.D.Gibbons : Nonparametric Inference
T.P.Hettmansperger : Statistical Inference based on ranks
C.R.Rao : Linear Statistical Inference and its Applications
E.L.Lehmann : Theory of Point Estimation
T.S.Ferguson : Mathematical Statistics
D.A.S.Fraser : Nonparametric methods in Statistics
J.O.Berger : Statistical Decision Theory and Bayesian Analysis
B.Efron : The Jackknife, the Bootstrap and other Sampling Plans
B.Efron : Bootstrap methods - another look at jackknife
B.Efron & R.J.Tibshirani : An Introduction to the Bootstrap
J.Shao & D.Tu : The Jackknife and Bootstrap

  •  Paper - VB : Stochastic Process and Time Series Analysis  
Stochastic Processes (35 marks)
Introduction to Stochastic Process, Markov Chains with finite and countable state space, Chapman-Kolmogorov equation, Classification of States, Calculation of n-step transition probability and its limit, Stationary distribution, Random walk, Martingales. (16)
Discrete state space continuous time Markov Chains, Poisson Process, Birth-Death Process, Renewal theory: Elementary Renewal theorem, Statement & uses of Key Renewal theorem. (12)
Branching Process: Galton Watson branching process, Probability of ultimate extinction, Distribution of Population size. (5)
Continuous process: Brownian motion. (2)

References :
S.Karlin and H.M.Taylor : A First Course in Stochastic Process, Vol-1
J Medhi : Stochastic Process
D.R.Cox : Renewal Theory
S.Ross : Stochastic Process
Basu A.K. : Stochastic Process
Hoel P.G., Port S.C. and Stone C.J : An Introduction to Stochastic Process
Bhattacharyya R.N and Waymire, E : Stochastic Processes and Applications

Time Series Analysis (15)
Stationary time series. Autocorrelation and partial autocorrelation functions. Correlogram. (7)
Forecasting techniques - Box-Jenkins Models. (4)
Spectral Analysis - Periodogram. (4)

References :
C.Chatfield : The Analysis of Time Series - An Introduction
G.E.P.Box,
G.M.Jenkins & G.C.Reinsel		 : Time Series Analysis - Forecasting and Control
A.Pankratz : Forecasting with Univariate Box-Jenkins Model
G. Jancek and L. Swift : Time Series - Forecasting, Simulation, Applications

  •  Paper - VIA : Applied Multivariate Analysis  
Multivariate linear regression model : estimation of parameters, tests of linear hypotheses, different test criteria, Multivariate Analysis of variance of one and two way classified data. Multivariate Analysis of Covariance. (12)
Hierarchical and non-hierarchical clustering methods. (6)
Classification and discrimination procedures for discrimination between two known populations - Bayes, Minimax and Likelihood Ratio procedures. Discrimination between two multivariate normal populations. Sample discriminant function. Likelihood ratio rule. Tests associated with discriminant function, Probabilities of misclassification and their estimation. Classification of several populations. Fisher’s method for discriminating among several populations. (10)
Population and sample principal components and their uses. Large sample inferences. (4)
The orthogonal factor model, Estimation of factor loading, Factor rotation, Estimation of Factor scores, Interpretation of Factor Analysis. (7)
Canonical variables and canonical correlations (population & sample) and their interpretations. Large sample inferences. (5)
Demonstration through statistical packages. (6)

References :
T.W.Anderson : An Intro. to Multivariate Statistical Analysis,
(2nd edition).
N.C.Giri : Multivariate Statistical Inference
R.A.Johnson. & D.W.Wichern : Applied Multivariate Statistical Analysis
A.M.Khirsagar : Multivariate Analysis
D.F.Morrison : Multivariate Statistical Methods
R.J.Muirhead : Aspects of Multivariate Statistical Theory
G.A.F.Seber : Multivariate Observations
S.C.Sharma : Applied Multivariate Techniques
M.S.Srivastava. & C.G.Khatri : An Introduction to Multivariate Statistics

  •  Paper - VIB : Generalized Linear Models and Data Analytic Techniques  
Types of data. Two-way classified data - Contingency Tables and associated distributions, Types of studies, Relative Risk and Odds Ratio and their properties. More-than-two-way classified data - partial associations, marginal and conditional odds. (5)
Generalized Linear Models - introduction, components of a generalized linear model, measuring the goodness of fit, deviance, residuals, maximum likelihood estimation. (5)
Applications to binary, count and polytomous data. Overdispersion. (12)
Ideas of marginal, conditional and quasi likelihoods. (2)
Longitudinal Data Analysis - introduction with motivation. (2)
Exploring longitudinal data. (4)
Linear models for longitudinal data -introduction, mean models, covariance models, mixed effects models. Predictions. (5)
Discrete longitudinal data- generalized linear marginal models, GEE for marginal models. (3)
Generalized linear subject specific models and transition models. (2)
Missing data patterns, Multivariate setup with one variable subject to non response, Missing data Mechanism. (2)
Quasi randomization inference for data with missing values, Imputation procedures: Mean imputation, hot deck, cold deck, regression imputation procedures. (5)
Maximum likelihood estimation for data with missing values - E.M. algorithm. (3)

References :
A.Agresti : Categorical Data Analysis
P.McCullagh & N.Nelder : Generalized Linear Models
R.J.A Little and D.B.Rubin : Statistical analysis with Missing data
P.J.Diggle, K.Y.Liang, S.Zeger, P.Heagerty : Analysis of Longitudinal Data, (2nd ed.)

  •  Module 1  
1. Advanced Statistical Inference
Invariant statistical decision problem and invariant decision rules. Equivariant estimation. Best invariant estimator in location and scale families. Best invariant estimator of a distribution function. Invariance in hypothesis testing. Uniformly most powerful invariant tests. (15)
Improved estimation of mean and dispersion under the normal set up. (6)
Behren-Fisher problem. Scheffe’s solution in the univariate case and its multivariate extension. Welch’s approach. Banerjee’s approach. (4)
Brownian Approximation and Truncated Tests, Tests with curved stopping boundaries Repeated significance tests, Fixed width interval estimation, Group sequential approach. (25)

References :
E.L.Lehmann : Theory of Point Estimation
E.L.Lehmann : Testing Statistical Hypotheses
R.J.Serfling : Approximation Theorems of Mathematical Statistics
R.Muirhead : Aspects of Multivariate Statistical Theory
D.Sigmund : Sequential Inference
J.Berger : Statist. Decision Theory - Foundation, Concepts & Methods
B.K.Ghosh : Sequential Tests of Statistical Hypotheses

2. Bayesian Analysis and Semiparametric Analysis
Bayesian Analysis (35)
Overview and comparison of the three paradigms - classical statistics, data analysis and Bayesian analysis. Relative advantages and disadvantages.  
Detailed study of Bayesian Analysis - choice of subjective priors, conjugate and other non-subjective priors.  
Bayesian Inference - estimation, testing, interval estimation and prediction for some common models and common priors.  
Hierarchical and Empirical Bayes. Bayesian Computation.  
Introduction to Dirichlet process prior.  
Bayesian approaches to regression models.  
Applications :Generalized linear Models and categorical data, Longitudinal Models, Time series Models and Panel Data, Survival and event history Models.  

References :
J.O.Berger : Statistical Decision Theory and Bayesian Analysis
C.P.Robert : The Bayesian Choice
P.McCullagh & A.J.Nelder : Generalized Linear Models

Semiparametric Models and their Analyses (15)
Single-Index-Models  
Generalised Partial Linear Models  
Generalized Additive Models  

References :
Härdle, Müller, Sperlich, Werwatz : Non- and Semiparametric Modelling
D. Ruppert, M.P. Wand and R.J. Carroll : Semiparametric Regression
W. Härdle : Applied Nonparametric Regression
P.J. Green and B.W. Silverman : Nonparametric Regression & Generalized Linear Models
J.L. Horowitz : Semiparametric methods in Econometrics
T. Hastie and R.Tibshirani : Generalized Additive Models
P. McCullagh and J. Nelder : A Generalized Linear Models, 2 edn
D.W. Scott : Multivariate Density Estimation:Theo., Prac. & Visualization
M.P. Wand and M.C. Jones : Kernel Smoothing
A. Yatchew : Semiparametric Regression for Applied Econometrician

3. Nonparametric Methods
Hodges-Lehmann Esimators, M, L and R - estimators, Projection Principle, Influence function. (20)
Nonparametric Regression (8)
Linear Rank Statistic and its asymptotic distribution under null and different local alternatives. Consistency and Asymptotic Relative efficiency. Optimality of tests. (20)
Bivariate sign test. (2)

References :
J.Hajek & Z.Sidek : Theory of Rank Tests
R.H.Randles & D.A.Wolfe : Introduction to the theory of nonparametric statistics
T.P.Hettmansperger : Statistical Inference based on ranks
E.L.Lehmann : Theory of Point Estimation

  •  Module 2  
1. Advanced Design of Experiments
PBIB designs.  
Optimum experimental designs.  
Weighing designs.  
Asymetric Factorial designs.  
Fractional Factorial designs.  
Response surface designs.  
Repeated Measurement designs.  

References :
D.Raghavarao : Construction and Combinatorial Problems in Design of Experiments
K.R.Shah
& B.K.Sinha		 : Theory of Optimal Designs
G.E.P.Box
& N.R.Draper		 : Empirical Model Building and Response Surfaces
A.I.Khuri
& J.A. Corneli		 : Response Surfaces
A.Hedayat : Survey of Design and Linear Models (ed. J.N.Srivastava)
J.Keifer : Annals of Mathematical Statistics (1958)
J.Keifer : A Survey of Statistical Designs and Linear Models
G.E.P.Box
& J.S,Hunter		 : Annals of Mathematical Statistics (1957)
R.C.Bose
& K.R.Nair		 : Sankhya (1939)
R.C.Bose
& T.Shimamoto		 : Journal of American Statistical Association (1952)
K.R.Nair & C.R.Rao : Journal of Royal Statistical Society,B (1948)
B.Kurkjian
& M.Zelen		 : Biometrika (1963)

2. Advanced Sample Survey
Unified theory of finite population sampling. Sampling design, sampling scheme and inclusion probabilities. Data and estimators - linear and linear unbiased estimators of population total / mean, Horvitz-Thompson estimator, Generalized Difference and Generalized Regression estimators, issues in non-negative variance estimation. πPS sampling schemes, Rao-Hartley-Cochran strategy.  
Non-existence of UMVUE. Existence / Non-existence of UMVLUE of a population total. Admissibility of estimators and strategies. Existence of UMVUE and MLE in scale-load approach. Concepts of sufficiency and likelihood in survey sampling. Rao-Blackwell theorem and its applications. Murthy’s unordering principle.  
Inference under super-population models. Optimal design -unbiased strategies and optimal model-unbiased prediction under simple regression models. Comparison of sampling strategies.  
Randomized response techniques. The Warner model and the unrelated question models. Randomized response models for variables.  
Estimation for domains - the basic estimation method, ratio and regression estimators for domains. Issues in small domain estimation - synthetic estimators.  

References :
C.M.Cassel, C.E.Sarndal.
& J.H.Wretman 		: Foundations of Inference in survey Sampling
A.Chaudhuri & R.Mukerjee : Randomized Response - theory and techniques
A.Chaudhuri & J.W.E.Vos : United Theory and Strategies of Survey Sampling
A.S.Hedayat & B.K.Sinha : Design and Inference in Finite Population Sampling
P.Mukhopadhyay : Inferential Problems in Survey Sampling
C.E.Sarndal., B.Swensson
& J.Wretman 		: Model assisted Survey Sampling

3. Advanced Multivariate Analysis
Parametric Inference : Spherical and elliptical distributions. Likelihood Ratio, Union-intersection and other methods of construction of Multivariate Tests - their Applications to Different Multivariate Testing Problems based on Normal Distributions. Associated confidence regions and simultaneous confidence intervals. Multivariate Behrens-Fisher Problem. Growth Curve Models. Robustness. Invariance. Unbiasedness and other optimum properties of Tests. Decision -theoretic Estimation of the Parameters of a Multivariate Normal Distribution  
Nonparametric Inference : Multivariate Single Sample Location Problem. Multivariate Two -sample and Multisample Problems for Location and Scale. Rank Tests for Independence. Estimation in Linear Models Based on Rank Tests.  

References :
R.J.Muirhead : Aspects of Multivariate Statistical Theory
M.S.Srivastava & C.G. Khatri : An Introduction to Multivariate Statistics
N.C.Giri : Multivariate Statistical Inference
T.W.Anderson : An Introduction to Multivaraite Statistical Analysis,
(2nd ed.)
A.M.Khirsagar : Multivariate Analysis
D.F. Morrison : Multivariate Statistical Methods
M.L Puri & P.K.Sen : Nonparametric Methods in Multivariate Analysis

3. Advanced Regression Analysis
Nonparametric methods in regression.  
Shrinkage estimator.  
Bayesian analysis in regression.  
Some variations in the standard regression models.  
Generalized Additive Models.  
Generalized Linear Mixed Models.  
Robust regression.  

References :
N.Draper & H.Smith : Applied Regression Analysis
H.D.Vinod & A.Ullah : Recent Advances in Regression Methods
P.McCullagh & A.J.Nelder : Generalized Linear Models
McCullough C. E. & S.R Searle : Generalized, Linear and Mixed Models, 2nd Edition
J.Rousseeuw & A.M.Leroy : Robust Regression & Outlier Detection
T. Hastie and R. Tibshirani : Generalized Additive Models

  •  Module 3  
1. Statistical Genomics and Bioassay
Statistical Genomics (35 marks)
Biological Introduction-basic concepts of Molecular genetics.  
Principle of Mendelian Inheritance.  
Population genetics.  
Segregation Analysis.  
Parametric linkage analysis.  
Non parametric Linkage analysis.  
QTL analysis.  

References :
C.C.Li : First Course on Population Genetics
W.J.Ewens : Mathematical Population Genetics
P.Nagylaki : Introduction to Theoretical Population Genetics
R.Durbin, S.R.Eddy,
A.Krogh & G.Mitchison		 : Biological Sequence Analysis
- Probabilistic Models of Proteins & Nucleic Acids

Bioassay (15 marks)
Logic of biological assay; dosage response curves; quantitative and quantal responses; parallel line and slope-ratio assays; simplified estimators; sequential assays; problem of design.  
PK/PD Models : Compartment models and their identifiability ,Numerical solutions of coupled differential equations, Mixed effects models and population PK/PD  

References :
Z.Govindarajulu : Statistical Techniques in Bioassay
D.J.Finney : Statistical Methods in Bioassay
D.J.Finney : Probit Analysis (3rd edition)

2. Survival Analysis & Clinical Trials
Survival Analysis (25 marks)
Introduction. Basic functions and Models.  
Censoring and Truncation.  
Topics in univariate Estimation : Parametric and Nonparametric Estimation.  
Regression models : Parametric and Semiparametric models - estimation.  
Regression Diagnostics.  
Frailty models.  
Competing Risk and Multivariate Survival models.  

References :
D.R.Cox & D.Oakes : Analysis of Survival Data
A.J.Gross & A.V.Clark : Survival Distribution-Reliability Appls. in Biomed. Sciences
R.G.Miller : Survival Analysis
P.J.Smith : Analysis of Failure and Survival Data
J.D.Kalbfleisch
& R.L.Prentiice		 : The Statistical Analysis of Failure Time Data
J.P.Klein
& M.L.Moeschberger 		: Survival Analysis: Techniques for Censored and Truncated Data

Clinical Trials (25 marks)
Introduction.  
Basic Study Design.  
Randomization and Blinding.  
Ethical Issues in Clinical Trials.  
Sample Size.  
Trial Conduct and Monitoring.  
Group sequential designs and interim stopping rules.  
Adaptive Designs.  
Issues in Data Analysis.  
Closeout, Reporting and Interpreting of Results.  
Meta-Analysis.  

References :
S.Piantadosi : Clinical Trials - A Methodologic Perspective
B.S.Everitt and A.Pickles : Statistical Aspects of Design & Analysis of Clinical Trials
S.J.Pocock : Clinical Trials
J.Whitehead : The Design and Analysis of Sequential Clinical Trials

3. Epidemiology
Study design : Descriptives, Case-Control Studies, Cohort Studies, Choice of study design.  
Assessing causality : Selection, Confounding, Validity and generalisability.  
Measures of Disease Frequency and Association.  
The analysis of epidemiological studies.  
Screening.  
Applications to Nutrition, Genetics, Environmental and occupational health.  
Other applications.  

References :
K.J.Rothman & S.Geenland : Modern Epidemiology
S.Selvin : Statistical Analysis of Epidemiologic Data
D.McNeil : Epidemiological Research Methods
J.F.Jekel, J.G.Elmore & D.L.Katz : Epidemiology, Biostatistics and Preventive Medicine
N.E.Breslow and N.E.Day : Statistical Methods in cancer Research, Vol. 1,
The Analysis of Case-Control Studies
N.E.Breslow and N.E.Day : Statistical Methods in cancer Research, Vol. 2,
The Design and Analysis of Cohort Studies

3. Demography
Coverage and content errors in demographic data .Use of balancing equation. Population composition. Adjustment of Age data- use of Whipple and Myer’s indices., dependency ratio, Measures of Migration and Urbanisation.  
Definition of concepts: Life and Death, Death Rates- age, space and cause specific. Adjusted death rates,  
Life tables: Distribution of life table functions and their estimates. Multiple Decrement tables.  
Natality: Birth rates- age-sex adjusted, Stochastic Models of fertility and Population growth, stable and quasi stable population, intrinsic growth rate.  
Population Estimation and Projection, Methods for Population projection.  
Stochastic Models for Migration, Social and Occupational Mobility based on Markov Chains - closed and open systems, Estimation of Measures of Mobility. Manpower planning Models.  

References :
D.J.Bartholomew : Stochastic Models for Social Processes
(3rd edition)
C.L.Chiang : Introduction to Stochastic Processes in Biostatistics
P.R.Cox : Demography
H.S.Shryock et.al. : The Methods and Materials of Demography

  •  Module 4  
1. Econometrics
Single-equation linear model - some variations.  
Nonparametric methods in econometrics.  
Simultaneous Equations - identification & estimation.  
Analysis of Panel Data.  
Bayesian Econometrics.  
Demand Analysis.  
Production Function Analysis.  
Analysis of some special econometric models.  

References :
J.Johnston : Econometric Methods
G.G.Judge, et.al. : The Theory and Practice of Econometrics
W.Greene : Econometric Analysis
A.Zellner : An Introduction to Bayesian Inference in Econometrics
E.Malinvaud : Statistical Methods in Econometrics
H.Wold & L.Jureen : Demand Analysis - a study in econometrics
P.Sankhayan : An Intro.to the Economics of Agricultural Production
M.Nerlove : Estimation & Identification of Cobb-Douglas Models
A.Pagan & A.Ullah : Non-parametric Econometrics

2. Advanced Time Series Analysis
Smoothing Techniques - forecasting based on it.  
Box-Jenkins Models - identification, estimation, diagnostic checking, forecasting.  
ARCH and GARCH Models.  
State Space Models.  
Some other time series models.  
Cointegration.  
Multiple Time Series.  
Spectral Analysis.  

References :
G.E.P.Box, G.M.Jenkins
& G.C.Reinsel		 : Time Series Analysis - Forecasting and Control
P.Brockwell & R.A.Davis : Time Series - Theory and Methods
W.A.Fuller : Introduction to Statistical Time Series (2nd edition)
G.Janacek & L.Swift : Time Series, Forecasting, Simulations & Applications
G.C.Reinsel : Elements of Multivariate Time Series Analysis

3. Applied Stochastic Models and Finance
Stochastic Models (25)
Renewal Theory: Regenerative processes, applications.  
Markov Chains: estimation of transition probabilities, tests for order.  
Brownian motion and geometric Brownian motion.  
Semi-markov processes and Markovian decision processes - introduction and applications.  
Martingales - Convergence Theorem, Applications.  

Finance (25)
Risk-free and risky assets. Contracts and options. Continuously compounded interest, present valuation, risk, risk-neutral valuation.  
Arbitrage: examples, contracts and options under no-arbitrage assumptions.  
Option Pricing: Cox-Ross-Rubinstein Binomial and Black-Scholes models.  
Elementary portfolio management, Value-at-risk.  

References :
S. Karlin and R. Taylor : A First Course on Stochastic Processes
B. R. Bhat : Stochastic Models - Analysis and Applications
S. M. Ross : Intro. to Mathematical Finance: Options and Other Topics
N. H. Bingham & R. Kiesel : Risk-Neutral Val. : Pricing & Hedging of Fin. Derivatives
V. S. Bawa, S. J. Brown, R. W. Klein : Estimation Risk and Optimal Portfolio Choice

3. Advanced Regression Analysis
(See Module 2)

  •  Module 5  
1. Elements of Statistical Quality Management and Reliability
Statistical Quality Management (25)
Control charts for extreme values. Moving average and exponentially moving average charts. Cu-sum charts using V-masks and decision intervals. Economic design of X-bar chart.  
Acceptance sampling plans for inspection by variables for two-sided specifications. Mil Std 105 plans. Continuous sampling plans of Dodge type and Wald-Wolfowitz type and their properties. Bayesian sampling plans.  
Capability indices Cp, CpK, Cpm and CpmK. Estimation of Cp and CpK. Distribution of Ĉp.  
QM System and ISO 9001 - brief exposition.  
Basic concepts of 6σ - DMAIC approach and the metrics used.  

Reliability (25)
Reliabilty concepts and measures, components and systems, coherent systems, reliability of coherent systems.  
Life-distributions, reliability function, hazard rate, common univariate life distributions - exponential, weibull, gamma, etc.. Bivariate exponential distributions. Estimation of parameters and tests in these models.  
Notions of aging - IFR, IFRA, NBU, DMRL and NBUE classes and their duals. Loss of memory property of the exponential distribution.  
Reliability estimation based on failure times in variously censored life-tests and in tests with replacement of failed items. Stress-strength reliability and its estimation.  

References :
D.C.Montogomery : Introduction to Statistical Quality Control
E.R.Ott : Process Quality Control
G.B.Wetherill : Sampling Inspection and Quality Control
G.B.Wetherill & D.W.Brown : Statistical Process Control - Theory and Practice
R.E.Barlow and F.Proscahn : Statistical Theory of Reliability and Life-Testing
J.F.Lawless : Statistical Models and Methods of Life-time data
L.J.Bain & Engelhardt : Statistical Analysis of Reliability and Life-testing Models
S.Zacks : Reliability Theory

2. Operations Research
Definition and Scope of Operations Research : phases in Operation Research, models and their solutions, decision-making under uncertainty and risk, use of different criteria, sensitivity analysis.  
Transportation and assignment problems. Bellman’s principle of optimality, general formulation, computational methods and application of dynamic programming.  
Decision-making in the face of competition, two-person games, pure and mixed strategies, existence of solution and uniqueness of value in zero-sum games, finding solutions in 2x2, 2xm and mxn games.  
Analytical structure of inventory problems, EOQ formula of Harris, its sensitivity analysis and extensions allowing quantity discounts and shortages. Multi-item inventory subject to constraints. Models with random demand, the static risk model. P and Q- systems with constant and random lead times.  
Queueing models - specification and effectiveness measures. Steady-state solutions of M/M/1 and M/M/c models with associated distributions of queue-length and waiting time. M/G/1 queue and Pollazcek-Khinchine result. Machine interference problem.  
Sequencing and scheduling problems. 2-machine n-job and 3-machine n-job problems with identical machine sequence for all jobs.  
Branch and Bound method for solving travelling salesman problem.  
Replacement problems - Block and age replacement policies.  
PERT and CPM - basic concepts. Probability of project completion.  

References :
H.A.Taha : Operational Research
F.S.Hillier & G.J.Leiberman : Introduction to Operations Research
Kanti Swarup, P.K.Gupta & M.M.Singh : Operations Research
D.T.Philips, A.Ravindran & J.Solberg : Operations Research
C.W.Churchman, R.L.Ackoff & E.L.Arnoff : Introduction to Operations Research
T.M.Starr & D.W. Miller : Inventory Control - Theory & Practice
L.Kleinrock : Queueing Systems
Sasieni,Yaspan & Friedman : Operations Research
Sasieni & Achoff : Operations Research

3. Statistical Process Control
Basic concept of process monitoring and control, process capability and process optimization.  
Capability indices - CP, CPK and CPM, estimation, confidence intervals and tests of hypotheses relating to capability indices for normally distributed characteristics.  
Multivariate Quality control, use of control ellipsoid and of utility functions.  
Quality at design stage, quality function deployment, failure mode and effect analysis. Conjoint analysis. System, parameter and tolerance designs. Planning and analysis of fractional factorial experiments.  
Basic ideas of response surface methodology and contour plots. Taguchi methods for off-line control.  
Quality systems - ISO 9000 standards. Concept of 6-sigma and the Define-Measure-Analyse-Improve-Control approach.  

References :
E.R.Ott : Process Quality Control
M.S.Phadke : Quality Engineering through Robust Design
G.B.Wetherill & D.W.Brown : Statistical Process Control - Theory and Practice
R.H.Myers & D.C.Montogomerry : Response Surface Methodology
J.Fox : Quality through Design
N.Logothetis : Managing Total Quality
H.J.Mittag & H.Rinne : Statistical Methods of Quality Assurance

3. Advanced Operations Research
Multi-stage decision processes and Dynamic Programming. Integer programming - branch and bound algorithm and cutting-plane algorithm. Multi-criterion and goal programming. Stochastic programming - quantile rules, two-stage programming. Use of fractional programming. Ramming.  
Non-zero sum games, co-operative and competitive games, equlibrium solutions and their existence in bi-matrix games. Nash equilibrium solution.  
s-S policy for inventory and its derivation in the case of exponential demand, multi-echelon inventory models, models with variable supply and models for perishable items, estimation of EOQ in some simple cases.  
Transient solution of M/M/1 queue, bulk queues, finite queues, queues in tandem, steady-state solutions of M/Ek/1 and Ek/M/1 queues, GI/G/1 queue and its solution, simulation of queues.  
Flows in networks, max-flow min-cut theorem.  
Dynamic programming approach for maintenance problems, replacement of items with long life.  

References :
G.Hadley : Non-linear and Dynamic Programming
K.G.Murthy : Linear and Combinatorial Programming
L.Kleinrock : Queueing Systems
T.L.Saaty : Elements of Queueing Theory with Applications
G.Hadley & T.M.Whitin : Analysis of Inventory Systems
M.K.Starr and D.W.Miller : Inventory Control - Theory and Practice
J.C.C.Mckinsey : Introduction to the Theory of Games
H.M.Wagner : Principles of O.R.with Applications to Managerial Decisions
D.Gross & C.M.Harris : Fundamentals of Queueing Theory

3. Optimization Techniques
Linear Programming - Charnes perturbation method. Generalized L.P.P.. Bounded variables, decomposition principle of Dantizg and Wolfe.  
Search methods - different search methods for the single and several variable(s).  
Genetic algorithms.  
Dynamic Programming.  
Integer programming - integer linear and mixed integer linear programming problems, Gomery’s cutting plane method, Branch and Bound method. Balas algorithm for zero-one programming.  
Non-linear programming - multivariate optimization with inequality constraints. Kuhn-Tucker conditions.  
Convex programming, Quadratic Programming - Wolfe’s algorithm and Beale’s algorithm.  
Stochastic programming - Charne’s constraints and their deterministic equivalence, E-, V- and Kataoka models, two-stage programming, wait and see approach.  
Goal pogramming - formulation of goal constraints, Partitioning algorithm.  

References :
G.Hadley : Non-linear and Dynamic Programming
K.G.Murthy : Linear and Combinatorial Programming
P.Whittle : Optimization under Constraints
- Theory and Applications of Non-linear Programming
S.S.Vajda : Probabilistic Programming
N.S.Kambo : Mathematical Programming Techniques
S.S.Rao : Optimization - Theory and Applications
K.V.Mittal : Optimization Methods
D.E. Goldberg : Genetic algorithms
M. Gen and R. Cheng : Genetic Algorithms and Engg. Designs
F. Glover and M. Laguna : Tabu Search
Michalewicz : Genetic Algorithms & Data Structure - Evolution Programs

3. Advanced Reliability
Coherent systems, cuts and paths, modular decomposition, bounds on system reliability, structural and reliability importance of components.  
Closures of IFR, IFRA, NBU, DMRL and NBUE classes under formation of coherent systems, convolutions and mixtures.  
Univariate shock models and life-distributions arising out of them, bivariate shock models, common bivariate exponential distributions and their properties.  
Maintenance and replacement policies, availability of repairable systems, modelling of a repairable system by a non-homogeneous Poisson process.  
Reliability growth models, probability plotting techniques, Hollander-Proschan and Deshpande tests for exponentiality, tests for HPP vs NHPP with repairable systems. Basic ideas of accelerated life-testing.  

References :
R.E.Barlow and F.Proschan : Statistical Theory of Reliability and Life-Testing
J.F.Lawless : Statistical Models and Methods of Life-time data
L.J.Bain & Engelhardt : Statistical Analysis of Reliability and Life-testing Models
S.Zacks : Reliability Theory
W.Nelson : Applied Life Data Analysis

View Detailed Syllabus of PART I