Multivariate Data Analysis

Syllabus: Analysis of Multivariate data: Multivariate data summarization, Plots. Univariate and multivariate analyses similarities. Special problems associated with multivariate analysis Dimensionality reduction.
Multivariate normal distribution: Elementary properties. Inference on mean vectors in multivariate populations Mahalanobis D2, Hotellings T2 ,MANOVA.
Principal Component Analysis:
PC Analysis based on the population covariance matrix, based on the sample covariance matrix; use of principal components.
Factor analysis: Module, communality, variance of a factor & total variance; estimation of Parameters, choosing number of factors; selection of loading rotation.
Discriminant Analysis and classification: Fishers discriminant function,classification rule based on expected cost of misclassification; rule for classifying into two normals/K normals.
Cluster analysis, Multidimensional scaling, Correspondence analysis: Similarity measures, clustering methods and algorithms; multidimensional scaling basic algorithm; correspondance analysis algebraic development, inertia, interpretation.
Conjoint analysis: Introduction, methods.
Methods for multivariate SPC: Multivariate control charts, Multivariate process capability analysis.
Multivariate Linear Regression: Multivariate Linear Regression Model, Least square Estimation. Tests and confidence Intervals, Model Adequacy checking, Problems of Multicollinearity, Ridge Regression, Principal component Regression.


Reference Texts:
1. Applied Multivariate Methods for Data Analysis: By Johnson D.E., Duxbury Press (1998)
2. Multivariate Data Analysis: By Hair, J.F. Jr., Anderson, R.E., Tatham, R.L. and Black, W.C.. Pearson Education (Fifth Edition) (2006)
3. Applied Multivariate Techniques: By Sharma S. Wiley (1996)
4. Multivariate Statistical Process Control with industrial Applications: By Mason, R.L. and Young, J.C. ASA SIAM Series in Statistics and Applied Probability (2001)
5. Marketing Research: By Malhotra, N. Prentice Hall (Fifth Edition) (2006)

https://www.isibang.ac.in/~adean/infsys/database/msqms/sqc/MDA.html

Operations Research II

Syllabus: Integer Linear Programming: Introduction to ILP, formulation, branch and bound and cutting plane methods for solving ILPs. Applications of ILP: assignment problem, traveling salesman problem, cutting stock and material optimization problems.
Dynamic Programming: Deterministic dynamic programming problems, Bellmans optimality principle, forward and backward approaches for solving dynamic programming problems.
Queueing Theory: Introduction to waiting line models, steady state behavior of M/M/1, M/M/C queues, the problem of machine interference problem and use of finite queueing tables, introduction to M/G/1 and M/G/C models. Inventory Control : Introduction; Design of inventory systems; Deterministic inventory systems; Stochastic inventory systems; Inventory control at multiple locations; Inventory management in practice.
Project Management: Introduction; Critical path method; PERT network analysis; Statistical analysis of project duration; Precedence diagramming method; Software tools for project management.
Simulation: Introduction; Basics of simulation; Simulation languages and software; Simulation projects.
Multiple Criteria Decision Making: Basic concepts; Multiple criteria methods for finite alternatives; Multiple criteria mathematical programming problems; Goal programming; Method of global criterion and compromise programming; Interactive methods; applications and software.


Reference Texts:
1. Operations Research and Management Science, Hand Book: Edited By A. Ravi Ravindran, CRC Press, Taylor & Francis Group (web site:http://www.taylorandfrancis.com).
2. Nonlinear Programming Theory and Algorithms: By Mokhtar S. Basaraa, Hanif D. Sherali and C. M. Shetty, second edition, John Wiley & Sons Inc., New Delhi.
3. Network Programming: By Katta Murty, Pretice Hall.
4. Handbook of Applied Optimization: edited By Panos M. Pardalos and Mauricio G. C. Resende, Oxford University Press (www.oup.com)
5. The Linear Complementarity Problem: By Cottle, Pang and Stone, Academic Press.

Reliability, Maintainability And Safety II

Syllabus: Reliability Improvement and Redundancy: Usefulness of redundancy; redundancy in system (with exponential components): parallel, r out of n system, standby, shared load.
Reliability Testing Demonstration and Acceptance: Life testing methods; estimation of parameters and reliability with standard probability models using complete and censored samples; properties of these estimators; confidence intervals; probability plot and graphical procedures for estimating the parameter; validation of model; life test acceptance sampling plans in exponential case; sequential life test in exponential case; non-parametric estimation of reliability.
Reliability of Repairable System: Types of repair: good-as-new, minimal; modeling failure processes: renewal process, Poisson process, non-homogeneous Poisson process.
System Effectiveness Measures: Serviceability, maintainability, repairability, availability, operational readiness; reliability and maintainability trade-off.
Fault Tree Analysis: Event tree; simple fault tree and its construction; mathematics of FTA; FMEA; carrying out FMEA with practical example.
Accelerated Life Test: Need for accelerated life test (ALT); acceleration factor and method: use-rate, temperature, voltage; Arrhenius model, Erying model, inverse power model.
Warranty Analysis: Role of warranty; quality improvement versus warranty; free-replacement warranty (FRW) and pro-rated warranty (PRW); warranty policy and cost; analysis of warranty policy some simple cases; automobile warranty (two-dimensional).


Reference Texts:
1. Reliability in Engineering Design: By Kapur K.C. and Lamberson L.R. (1977), John Wiley & Sons, Inc.
2. Repairable System Reliability: By Ascher H. and Feingold H. (1984), Marcel Dekker.
3. Statistical Methods for Reliability Data: By Meeker W.Q. and L.A. Escobar L.A. (1998), John Wiley & Sons, Inc.
4. Warranty Cost Analysis: By Blischke W.R. and Prabhakar Murthy D.N. (1994), Marcel Dekker.
5. Concepts in Reliability: By Srinath L.S. (1975), Affiliated East-West Press Pvt. Ltd.
6. System Reliability Theory: By Hoyland A. and Rausand M. (1994), John Wiley & Sons, Inc.
7. Statistical Theory of Reliability and Life Testing: By Barlow R.E. and Proschan F. (1975), Holt, Rinehart and Winston, Inc.

https://www.isibang.ac.in/~adean/infsys/database/msqms/sqc/RMS2.html

Advanced Statistical Process Control

Syllabus: Advanced SPC Techniques: Dominance System Concept of Process & dominance patterns with examples, also explain the different types of process control techniques to be used in each case with examples & exercises. Process Capability calculation for Non Normal, Clemants method. Implementing Control Chart and Out of Control Action Plan Steps for implementation of control chart for on line process monitoring with out of control action plan. Group control chart for multiple stream processes. Control chart for short run processes. Interface and integration between SPC and EPC (Engineering Process Control. Multivariate Control Chart Formation, examples with exercises.

Taguchis On line QC Technique: Taguchis Loss Function and quality level definition & calculation of loss function for different types of quality characteristics. On line quality control system and method of process improvement calculation of beta correction factor by ANOVA method & implementation of the same with examples & exercises.
Acceptance Sampling: Continuous Sampling Plans (CSP1, CSP2), Multilevel Plans. Special purpose plans Chain Sampling and Skip lot sampling plans. Introduction to Bayesian sampling plans use of past data Using Military standards for multiattribute situation- recent development.


Reference Texts:
1. Introduction to statistical quality control: By D.C. Montgomery 4th Edition, John Wiley & Sons.Inc.
2. Multivariate Q C in Encyclopedia of statistical sciences, Vol. 6: Edited by WL Johnson, S Kotz, John Wiley, N.Y.
3. Quality Control and Industrial Statistical: By A J Duncan, 5th Edition, Irwin, Homewood, Ille.
4. Principle of Quality Control: By Jery Banks, John Wiley.
5. Encyclopedia and Handbook of Process Capability Indices - A Comprehensive Exposition of Quality Control Measures-Series on Quality, Reliability and Engineering Statistics Vol. 12: By W. L. Pearn and Samuel Kotz, World Scientific Publishing Co. Pte. Ltd. ( Available on line ) [ Addition]

https://www.isibang.ac.in/~adean/infsys/database/msqms/sqc/SPC2.html

Statistics for Decision Making II

Syllabus: Introduction: Principles of Statistical Inference. Formulation of the problems with examples.
Estimation: Point estimation, Estimator and Estimate, Criteria for good estimates Unbiasedness, Consistency, Efficiency and Sufficiency, Illustrations. Methods of estimation of Parameters of standard distributions. Interval estimation by examples Confidence internals of the parameters of the standard distributions. Estimation using Statistical Software.
Testing hypothesis: Formulation of the problem and concepts for evaluation of tests, Illustrations. Statistic, Sampling distributions of statistic and its Standard Error. Large sample tests in one and two sample problems of standard probability distributions, Statement of central limit theorem, Determination of sample size. Simple linear regression and correlation and corresponding confidence intervals. Transformation of statistics to stabilize the residual plots. Assessment of the model. Fitting of nonlinear regression using transformation. Analysis of categorical data. Pearsonian chisquare and its applications. Test of hypothesis using Statistical Software.
Linear Statistical Models: Definition of linear model, interactions with illustrations. One way and two way analysis of variance. ANOVA using Statistical Software.
Nonparametric Inference: Comparison with parametric inference, Use of order statistics. Sign test, Wilcoxon signed rank test, Mann Whitney test, Run test, Kolmogorov Smirnov test. Spearmans and Kendalls test.
Usage of statistical software


Pattern Recognition

Syllabus: Elements of Image processing and Analysis: Biology and physics of image formation and recognition-Digital images. Components of image processing system sensors, digitizer, processers, display unit, and hard copier. Mathematical preliminaries required vector algebra, orthogonal transformations, probability and statistics, fuzzy sets and properties, and mathematical morphology. Image processing Greyvalue histograms, Greyvalue distributions & statistics, thresholding & segmentation; Point operations Histogram transforms, pixels, gridding & quantization; Patterns and classes; image enhancement, image smoothening, image sharpening, image restoration, image compression, and image registration. Image analysis image segmentation, edge and line detection, feature extraction, and description. Recognition deterministic approaches, statistical approaches, fuzzy mathematical approach, syntactic approach, and morphological approaches.
Statistical and Fuzzy Mathematical Approach Pattern Recognition: Bayesian decision theory; Maximum likelihood and parameter estimation; Nonparametric techniques; Qualifying structure in pattern description and recognition; Grammar based approach; Neural pattern recognition.
Structural and Syntactic Pattern Recognition:
Segmentation: Detection of discontinuities Pont, Line, Edge and Combined detection; Edge linking and boundary detection Local processing, Global processing via Hough transform and Graph Theoretic techniques; Thresholding Foundation, The role of illumination, Simple Global Thresholding, Optimal Thersholding, Thershold selection based on boundary characteristics, thresholds based on several variables; Region-Oriented segmentation Basic formulation, region growing by pixel aggregation, region splitting and merging, morphologic segmentation, watersheds; The use of Motion in Segmentation spatial and frequency domain techniques; Texture segmentation pattern spectra and Granulometries.
Boundary and Region Representation and Description: Representation and Description: Representation schemes chain codes, polygonal approximations, signatures, boundary segments, the skeleton of a region; Boundary descriptors Simple descriptors, shape numbers, Fourier descriptors, moments; Regional descriptors simple descriptors, topological descriptors, texture, moments; Morphology Dilation, erosion, opening, closing, Hit or Mist Transform, basic morphological algorithms, extensions to grayscale images; Relational Descriptors. Recognition and Interpretation: Decision Theoretic Methods Matching (Minimum distance classifier, Matching by correlation); Optimum statistical classifier (Foundation, Bayes classifier for Gaussian pattern classes); Neural networks (Background, perceptron for two pattern classes, training algorithms, multiplayer feedforward neural networks). Structural methods: match shape numbers, string matching, syntactic methods. Interpretation: Object measurements Size, shape and orientation: Statistics of size distributions, resolution and scale; shape analysis, orientational statistics; Stereological models and microstructural analysis; Analysis of 3D data sets

Reference Texts:
1. Pattern Classification: By Duda RO, PE Hart and DG Stork, John Wiley & Sons, NY, 2nd Ed, 2001.
2. Structural Pattern Recognition: By T. Pavlidis, Springer Verlag, NY, 1977.
3. Image analysis and Mathematical Morphology: By J. Serra, Academic Press, 1982.
4. Digital Image Processing: By RC Gonzalez and RE Woods, Addison Wesley Publishing Company, 1992.
5. Digital Image Processing and Analysis: By B. Chanda and D. Dutta Majumdar, Prentice Hall, India.
6. Fuzzy Mathematical Approaches to Pattern Recognition: By S. K. Pal, and D. Dutta Majumdar, Wiley.

https://www.isibang.ac.in/~adean/infsys/database/msqms/sqc/PR.html

Neural Network

Syllabus: Introduction to Soft Computing and ANN: An overview of analysis and Design of intelligent systems using soft computing techniques, Basic Concepts of Artificial Neural Network (ANN), Similarity with biological neurons, General characteristics, Historical development and domain specific applications, Statistical modeling and ANN.
Building blocks of ANN and Fundamental ANN Models: Architecture, Weights, Bias, Net Input, Threshold, Activation functions, Training and its related parameters, Simulation. McCulloch-Pitts and Hebb Nets: architecture and algorithms with examples.
Learning Rules of ANN: Hebbian, Perceptron, Delta, Competitive, Perceptron convergence theorem.
Typical Networks: Single Layer Perceptron - architecture, training and application algorithm. Adaline and Madaline - architecture, training and application algorithm Discrete Hopfield Net - architecture, training and application algorithm.
Feed Forward Networks: Multi Layer Perceptron (MLP) - Generalized Delta (Back Propagation) Learning rule, architecture, training algorithm, selection of parameters, learning constraints, application algorithm, local optimum, merits and demerits, applications.
Radial Basis Function (RBF) - architecture, training algorithm.
Self Organizing Map: Kohonen Self Organizing Feature Maps (SOM) - architecture, training algorithm. Learning Vector Quantization (LVQ) - architecture, training algorithm.
Some Special Purpose Networks: Ensemble networks - purpose and concepts. Adaptive Resonance Theory (ART) - architecture, training algorithm, ART 1, ART 2. Probabilistic Neural Network (PNN) - architecture, training algorithm. Modular Networks. Case Studies.
Use of Software: Developing ANN models with the help of computer software such as MATLAB, STATISTICA, NEUROMAT etc. for solving real-life problems and related performance measures with graphical interface.


Reference Texts:
1. An Introduction to Neural Networks: By K. Gurney, UCL Press.
2. Computational Intelligence: By Andries P Engelbrecht, John Wiley & Sons Ltd., 2003.
3. Neural Networks, Fuzzy Logic and Genetic Algorithms: By S. Rajasekaran and G.A.V.Pai, PHI.
4. Neural Network Fundamentals, 1996: By N.K. Bose, P. Liung:, McGraw Hill Inc.,
5. Neural Networks, 1994: By Haykin Simon, Macmilan, U.K
6. Neural networks for pattern recognition, 1995: By Bishop, C., Oxford Univ. press
7. Neural networks for statistical modeling: By Murray Smith.
8. Neuro-Fuzzy PR-Methods in Soft Computing: By Sankar K.Pal and Sushmita Mitra, John Wiley & Sons

https://www.isibang.ac.in/~adean/infsys/database/msqms/sqc/NN.html